Question Bank for JEE Main & Advanced Physics Alternating Current / प्रत्यावर्ती धारा Self Evaluation Test - Alternating Current

1)

If an LCR series circuit is connected to an ac source, then at resonance the

A)

voltage across R is zero

B)

voltage across R equals the applied voltage

C)

voltage across C is zero

D)

voltage across L equals the applied voltage

View Solution

2)

Of the following about capacitive reactance which is correct?

A)

The reactance of the capacitor is directly proportional to its ability to store charge

B)

Capacitive reactance is inversely proportional to the frequency of the current

C)

Capacitive reactance is measured in farad

D)

The reactance of a capacitor in an A.C. circuit is similar to the resistance of a capacitor in a D.C. circuit

View Solution

3)

Which one of the following curves represents the variation of impedance (Z) with frequency f in series LCR circuit?

A)

B)

C)

D)

View Solution

4)

The power factor in a circuit connected to an A.C. The value of power factor is

A)

unity when the circuit contains an ideal inductance only

B)

unity when the circuit contains an ideal resistance only

C)

zero when the circuit contains an ideal resistance only

D)

unity when the circuit contains an ideal capacitance only

View Solution

5)

Which of the following graphs represents the correct variation of capacitive reactance \[{{X}_{C}}\] with frequency v?

A)

B)

C)

D)

View Solution

6)

Current in an ac circuit is given by\[i=3\,\sin \,\omega t+4\,\cos \,\omega t\] then

A)

rms value of current is 5 A

B)

mean value of this current in one half period will be \[6/\pi \]

C)

if voltage applied is \[V={{V}_{m\,}}\sin \,\omega t\] then the circuit must be containing resistance and capacitance.

D)

if voltage applied is \[V={{V}_{m}}\,\sin \,\omega t\], the circuit may contain resistance and inductance.

View Solution

7)

If we increase the driving frequency in a circuit with a purely capacitive load, then

A)

amplitude\[{{V}_{C}}\]increases

B)

amplitude\[{{V}_{C}}\]decreases

C)

amplitude\[{{i}_{C}}\]increases

D)

amplitude\[{{i}_{C}}\]decreases

View Solution

8)

If a direct current of value ampere is superimposed on an alternative current\[I=b\,\sin \,\omega t\] flowing through a wire, what is the effective value of the resulting current in the circuit?

A)

\[{{\left[ {{a}^{2}}-\frac{1}{2}{{b}^{2}} \right]}^{1/2}}\]

B)

\[{{\left[ {{a}^{2}}+{{b}^{2}} \right]}^{1/2}}\]

C)

\[{{\left[ \frac{{{a}^{2}}}{2}+{{b}^{2}} \right]}^{1/2}}\]

D)

\[{{\left[ {{a}^{2}}+\frac{{{b}^{2}}}{2} \right]}^{1/2}}\]

View Solution

9)

In a series LCR circuit, the difference of the frequencies at which current amplitude falls to\[\frac{1}{\sqrt{2}}\] of the current amplitude at resonance is

A)

\[\frac{R}{2\pi L}\]

B)

\[\frac{R}{\pi L}\]

C)

\[\frac{2R}{\pi L}\]

D)

\[\frac{3R}{2\pi L}\]

View Solution

10)

If\[{{i}_{1}}=3\,\sin \,\omega t\]and\[{{i}_{2}}=4\,\cos \,\omega t\], then\[{{i}_{3}}\]is

A)

\[5\,\sin \,(\omega t+{{53}^{o}})\]

B)

\[5\,\sin \,(\omega t+{{37}^{o}})\]

C)

\[5\,\sin \,(\omega t+{{45}^{o}})\]

D)

\[5\,\cos \,(\omega t+{{53}^{o}})\]

View Solution

11)

A sinusoidal voltage V(t) = 100 sin (500t) is applied across a pure inductance of L=0.02H. The current through the coil is:

A)

\[10\,\cos \,(500\,t)\]

B)

\[-10\,\cos \,(500\,t)\]

C)

\[10\,\sin \,(500\,t)\]

D)

\[-10\,\sin \,(500\,t)\]

View Solution

12)

Figure shows one cycle of an alternating current with the segments AB, BC, CD, DE being symmetrical and parabolic. The root mean square value of this current over one cycle is x mA, find x.

A)

1mA

B)

2mA

C)

3mA

D)

4mA

View Solution

13)

In given circuit capacitor initially uncharged. Now at t=0 switch S is closed then current given by source at any time t is

A)

\[\frac{2}{R}\left( 1-{{e}^{\frac{-2t}{CR}}} \right)\]

B)

\[\frac{\varepsilon }{2R}\left( 1+{{e}^{\frac{-2t}{CR}}} \right)\]

C)

\[\frac{\varepsilon }{2R}\left( 1-{{e}^{\frac{-2t}{CR}}} \right)\]

D)

\[\frac{2\varepsilon }{R}\left( 1-{{e}^{\frac{-2t}{CR}}} \right)\]

View Solution

14)

The transformer voltage induced in the secondary coil of a transformer is mainly due to

A)

a varying electric field

B)

a varying magnetic field

C)

the vibrations of the primary coil

D)

the iron core of the transformer

View Solution

15)

A coil of inductance 8.4 mH and resistance \[6\,\Omega \] is connected to a 12 V battery. The current in the coil is 1.0 A at approximately the time

A)

500s

B)

25s

C)

35ms

D)

1ms

View Solution

16)

Resonance frequency of a circuit is f. If the capacitance is made 4 times the initial value, the resonance frequency will become :

A)

\[f/2\]

B)

2f

C)

f

D)

f/4

View Solution

17)

The current (7) in the inductance is varying with time according to the plot shown in figure.

Which one of the following is the correct variation of voltage with time in the coil?

A)

B)

C)

D)

View Solution

18)

The voltage of an ac supply varies with time (t) I as\[V=120\,\sin \,100\pi \,t\,\cos \,100\pi t\]. The maximum voltage and frequency respectively are

A)

120 volts, 100 Hz

B)

\[\frac{120}{\sqrt{2}}volts,\,\,100Hz\]

C)

60 volts, 200 Hz

D)

60 volts, 100 Hz

View Solution

19)

The equation of AC voltage is\[E=220\,\sin \,(\omega t+\pi /6)\] and the A.C. current\[I=10\,\sin \,(\omega t+\pi /6)\]. The average power dissipated is

A)

150 W

B)

550 W

C)

250 W

D)

50 W

View Solution

20)

In an L-R circuit, the value of L is \[(0.4/\pi )\]henry and the value of R is 30 ohm. If in the circuit, an alternating emfof200 volt at 50 cycles per second is connected, the impedance of the circuit and current will be:

A)

11.4 ohm, 17.5 ampere

B)

30.7 ohm, 6.5 ampere

C)

40.4 ohm, 5 ampere

D)

50 ohm, 4 ampere.

View Solution

21)

In an ac circuit an alternating voltage e=200 \[\sqrt{2}\,\sin \,100\,t\] volts is connected to a capacitor of capacity \[1\,\mu F\]. The r.m.s. value of the current in the circuit is

A)

10 mA

B)

100 mA

C)

200 mA

D)

20 mA

View Solution

22)

Determine the rms value of a semi-circular current wave which has a maximum value of a.

A)

\[(1\sqrt{2})a\]

B)

\[(\sqrt{3/2})a\]

C)

\[(\sqrt{2/3})a\]

D)

\[(\sqrt{1/3})a\]

View Solution

23)

The r.m.s. value of potential difference V shown in the figure is

A)

\[{{V}_{0}}\]

B)

\[{{V}_{0}}/\sqrt{2}\]

C)

\[{{V}_{0}}/2\]

D)

\[{{V}_{0}}/\sqrt{3}\]

View Solution

24)

The equation of alternating current is :

\[I=50\sqrt{2}\,\sin \,400\pi t\,amp\]. Then the frequency and root mean square of current are respectively

A)

\[200\text{ }Hz,\text{ }50\text{ }amp\]

B)

\[400\pi \,Hz,\,\,50\sqrt{2}\,\,\,amp\]

C)

\[200\,Hz,\,\,\,50\sqrt{2}\,\,amp\]

D)

\[50\text{ }Hz,\text{ }200\text{ }amp\]

View Solution

25)

A coil has resistance 30 ohm and inductive reactance 20 ohm at 50 Hz frequency If an ac source, of 200 volt, 100 Hz, is connected across the coil, the current in the coil will be

A)

4.0 A

B)

8.0 A

C)

\[\frac{20}{\sqrt{13}}\,A\]

D)

2.0 A

View Solution

26)

A small signal voltage\[V(t)={{V}_{0}}\,\sin \,\omega t\]is applied across an ideal capacitor C:

A)

Current I (t), lags voltage V (t) by \[90{}^\circ \].

B)

Over a fall cycle the capacitor C does not consume any energy from the voltage source.

C)

Current I (t) is in phase with voltage V (t).

D)

Current I (t) leads voltage V (t) by \[180{}^\circ \].

View Solution

27)

An ac voltage is applied to a resistance R and an inductor L in series. If R and the inductive reactance are both equal to \[3\,\Omega \], the phase difference between the applied voltage and the current in the circuit is

A)

\[\pi /6\]

B)

\[\pi /4\]

C)

\[\pi /2\]

D)

zero

View Solution

28)

The voltage time (V-t) graph for triangular wave having peak value \[{{V}_{0}}\] is as shown in figure.

The rms value of V in time interval from t=0 to T/4 is

A)

\[\frac{{{V}_{0}}}{\sqrt{3}}\]

B)

\[\frac{{{V}_{0}}}{2}\]

C)

\[\frac{{{V}_{0}}}{\sqrt{2}}\]

D)

\[\frac{{{V}_{0}}}{3}\]

View Solution

29)

An inductor 20 mH, a capacitor \[50\,\mu F\]and a resistor \[40\Omega \] are connected in series across a source of emf V=10 sin 340 t. The power loss in A.C. circuit is:

A)

0.51 W

B)

0.67 W

C)

0.76 W

D)

0.89 W

View Solution

30)

A series R-C circuit is connected to an alternating voltage source. Consider two situations:

When capacitor is air filled.

When capacitor is mica filled.

Current through resistor is i and voltage across capacitor is V then:

A)

\[{{V}_{a}}>{{V}_{b}}\]

B)

\[{{i}_{a}}>{{i}_{b}}\]

C)

\[{{V}_{a}}={{V}_{b}}\]

D)

\[{{V}_{a}}<{{V}_{b}}\]

View Solution

31)

Find the current passing through battery immediately after key (K) is closed. It is given that initially all the capacitors are uncharged. (given that \[R=6\,\Omega \] and \[C=4\mu F\])

A)

1 A

B)

5 A

C)

3 A

D)

2 A

View Solution

32)

A resistance 'R' draws power 'P' when connected to an AC source. If an inductance is now placed in series with the resistance, such that the impedance of the circuit becomes 'Z', the power drawn will be

A)

\[P\sqrt{\frac{R}{Z}}\]

B)

\[P\left( \frac{R}{Z} \right)\]

C)

P

D)

\[P{{\left( \frac{R}{Z} \right)}^{2}}\]

View Solution

33)

A condenser of capacity C is charged to a potential difference of \[{{V}_{1}}\]. The plates of the condenser are then connected to an ideal inductor of inductance L. The current through the inductor when the potential difference across the condenser reduces to \[{{V}_{2}}\] is

A)

\[{{\left( \frac{C(V_{1}^{2}-V_{2}^{2})}{L} \right)}^{1/2}}\]

B)

\[{{\left( \frac{C{{({{V}_{1}}-{{V}_{2}})}^{2}}}{L} \right)}^{1/2}}\]

C)

\[\frac{C(V_{1}^{2}-V_{2}^{2})}{L}\]

D)

\[\frac{C({{V}_{1}}-{{V}_{2}})}{L}\]

View Solution

34)

For the circuit as shown in figure; the applied Current in A.C. circuit is zero ampere and\[{{I}_{C}}=10A\]. Then the magnitude of current \[{{I}_{L}}\]is

A)

4 A

B)

10 A

C)

5 A

D)

undefined

View Solution

35)

What is the value of inductance L for which the current is maximum in a series LCR circuit with \[C=10\mu F\] and \[\omega =1000{{s}^{-1}}\]?

A)

1 mH

B)

cannot be calculated unless R is known

C)

10 mH

D)

100 mH

View Solution

36)

In the circuit shown, the symbols have their usual meanings. The cell has emf E. X is initially joined to V for a long time. Then, disjoined to Z The maximum charge on C at any later time will be

A)

\[\frac{E}{R\sqrt{LC}}\]

B)

\[\frac{ER}{2\sqrt{LC}}\]

C)

\[\frac{E\sqrt{LC}}{2R}\]

D)

\[\frac{E\sqrt{LC}}{R}\]

View Solution

37)

A coil of inductive reactance \[31\,\Omega \]has a resistance of \[8\,\Omega \]. It is placed in series with a condenser of capacitive reactance \[25\,\Omega \]. The combination is connected to an a.c. source of 110 volt. The power factor of the circuit is

A)

0.64

B)

0.80

C)

0.33

D)

0.56

View Solution

38)

The two capacitors, shown in the circuit, are initially uncharged and the cell is ideal. The switch S is closed at t=0. Which of the following functions represents the current i(t) through the cell as a function of time? Here\[{{i}_{0}},\,{{i}_{1}},\,{{i}_{2}}\]are constants.

A)

\[i(t)={{i}_{0}}+{{i}_{1}}{{e}^{-t/\tau }}\]; \[\tau =3C\times \frac{R}{3}\]

B)

\[i(t)={{i}_{0}}+{{i}_{1}}{{e}^{-t/\tau }}+{{i}_{2}}{{e}^{-t/2\tau }}\]; \[\tau =RC\]

C)

\[i(t)={{i}_{1}}+{{i}_{1}}{{e}^{-t/\tau }}\]; \[\tau =3C\times \frac{R}{3}\]

D)

\[i(t)={{i}_{0}}+{{i}_{1}}{{e}^{-t/\tau }}\]; \[\tau =3RC\]

View Solution

39)

A coil of 40 henry inductance is connected in series with a resistance of 8 ohm and the combination is joined to the terminals of a 2 volt battery. The time constant of the circuit is

A)

20 seconds

B)

5 seconds

C)

1/5 seconds

D)

40 seconds

View Solution

40)

A resistor and an inductor are connected to an ac supply of 120 V and 50 Hz. The current in the circuit is 3 A. If the power consumed in the circuit is 108 W, then the resistance in the circuit is

A)

\[12\,\Omega \]

B)

\[40\,\Omega \]

C)

\[\sqrt{(52\times 25)}\Omega \]

D)

\[360\,\Omega \]

View Solution

41)

A short-circuited coil is placed in a time-varying magnetic field. Electrical power is dissipated due to the current induced in the coil. If the number of turns were to be quadrupled and the wire radius halved, the electrical power dissipated would be

A)

equal

B)

the same

C)

doubled

D)

quadrupled

View Solution

42)

An LCR series circuit with \[100\,\Omega \] resistance is connected to an AC source of 200 V and angular frequency 300 radians per second. When only the capacitance is removed, the current lags behind the voltage by \[60{}^\circ \]. When only the inductance is removed, the current leads the voltage by \[60{}^\circ \]. Then the current and power dissipated in LCR circuit are respectively

A)

1A, 200 watt

B)

1A, 400 watt

C)

2A, 200 watt

D)

2A, 400 watt

View Solution

43)

In the circuits and switches\[{{S}_{1}}\]and\[{{S}_{2}}\]are S closed at t=0 and are kept closed for a long time The variation of current in the two circuits for\[t\ge 0\]are roughly shown by figure (figures are schematic and not drawn to scale):

A)

B)

C)

D)

View Solution

44)

A coil has an inductance of 0.7 henry and is joined in series with a resistance of \[220\,\Omega \]. When the alternating emf of 220 V at 50 Hz is applied to it then the phase through which current lags behind the applied emf and the watt less component of current in the circuit will be respectively

A)

\[30{}^\circ ,\text{ }1\text{ }A\]

B)

\[45{}^\circ ,\text{ }0.5\text{ }A\]

C)

\[60{}^\circ ,\text{ }1.5\text{ }A\]

D)

None of these

View Solution

45)

In an L-C circuit shown in the figure, C=1F, L=4H at time t=0, charge in the capacitor is 4C and it is decreasing at a rate of\[\sqrt{5}\,C/s\]. Choose the correct statements.

A)

maximum charge in the capacitor can be 6C

B)

maximum charge in the capacitor can be 8C

C)

charge in the capacitor will be maximum after time \[2\,{{\sin }^{-1}}\](2/3) sec

D)

None of these

View Solution

46)

Charges on the capacitors in four oscillating LC circuits vary as follows: (1) q=2 cos 4t, (2) q =4 cos t, (3) q = 3 cos 4t, (4) q = 4 cos 2t, with q in coulomb and t in second. In which circuit(s) current amplitude is greatest?

A)

(1)

B)

(2)

C)

(3)

D)

(4)

View Solution

47)

Figure shows a source of alternating voltage connected to a capacitor and resistor. Which of the following phasor diagrams correctly secrobes the phase relationship between\[{{I}_{c}}\], the current between the source and the capacitor, and\[{{I}_{R}}\], the current in the resistor?

A)

\[\begin{align} & \xrightarrow{{{I}_{c}}} \\ & \xrightarrow[{{I}_{R}}]{} \\ \end{align}\]

B)

\[\xleftarrow{{{I}_{C}}}\xrightarrow{{{I}_{R}}}\]

C)

D)

View Solution

48)

A capacitor of\[10\,\mu F\]and an inductor of 1 H are joined in series. An ac of 50 Hz is applied to this combination. What is the impedance of the combination?

A)

\[\frac{5({{\pi }^{2}}-5)}{\pi }\Omega \]

B)

\[\frac{{{10}^{2}}(10-{{\pi }^{2}})}{\pi }\,\Omega \]

C)

\[\frac{10({{\pi }^{2}}-5)}{\pi }\,\Omega \]

D)

\[\frac{{{5}^{2}}(10-{{\pi }^{2}})}{\pi }\Omega \]

View Solution

49)

What is the amount of power delivered by the ac source in the circuit shown (in watts).

A)

500 watt

B)

1014 watt

C)

1514 watt

D)

2013 watt

View Solution

50)

The current in an L-R circuit builds up to\[{{(3/4)}^{th}}\]of its steady state value in 4 seconds. The time constant of this circuit is

A)

\[\frac{1}{ln\,\,2}\sec \]

B)

\[\frac{2}{ln\,\,2}\sec \]

C)

\[\frac{3}{ln\,\,2}\sec \]

D)

\[\frac{4}{ln\,\,2}\sec \]

View Solution

51)

A resistor of resistance R, capacitor of capacitance C and inductor of inductance L are connected in parallel to AC power source of voltage \[{{\varepsilon }_{0}}\,\sin \,\omega t\]. The maximum current through the resistance is half of the maximum current through the power source. Then value of R is

A)

\[\frac{\sqrt{3}}{\left| \left. \omega C-\frac{1}{\omega L} \right| \right.}\]

B)

\[\sqrt{3}\left. \left| \frac{1}{\omega C}-\omega L \right. \right|\]

C)

\[\sqrt{5}\left. \left| \frac{1}{\omega C}-\omega L \right. \right|\]

D)

None of these

View Solution

52)

When the rms voltages \[{{V}_{L}}\], \[{{V}_{C}}\] and \[{{V}_{R}}\]are measured respectively across the inductor L, the capacitor C and the resistor R in a series LCR circuit connected to an AC source, it is found that the ratio \[{{V}_{L}}:{{V}_{C}}:{{V}_{R}}=1:2:3\]. If the rms voltage of the AC sources is 100 V, the \[{{V}_{R}}\] is close to:

A)

50V

B)

70V

C)

90V

D)

100V

View Solution

53)

Time constant of L-R circuit will be

A)

\[\frac{L}{R}\]

B)

\[\frac{2L}{R}\]

C)

\[\frac{L}{2R}\]

D)

None of these

View Solution

54)

A series LR circuit is connected to an ac source of frequency \[\omega \] and the inductive reactance is equal to 2R. A capacitance of capacitive reactance equal to R is added in series with L and R. The ratio of the new power factor to the

A)

\[\sqrt{\frac{2}{3}}\]

B)

\[\sqrt{\frac{2}{5}}\]

C)

\[\sqrt{\frac{3}{2}}\]

D)

\[\sqrt{\frac{5}{2}}\]

View Solution

55)

LC circuit contains a 20 mH inductor and a \[50\,\mu F\]capacitor with an initial charge of 10 mC. The resistance of the circuit is negligible. Let the instant the circuit is closed at t=0. At what time is the energy stored completely magnetic?

A)

t=0

B)

t=1.57 ms

C)

t=3.14 ms

D)

t= 6.28 ms

View Solution

56)

An inductor \[20\times {{10}^{-3}}\] Henry, a capacitor \[100\,\mu F\]and a resistor \[50\,\Omega \] are connected in series across a source of EMF V=10 sin 314t. If resistance is removed from the circuit and the value of inductance is doubled, then the variation of current with time in the new circuit is -

A)

\[0.52\text{ }cos\text{ }314t\]

B)

\[0.52\text{ }sin\text{ }314t\]

C)

\[0.52\,\sin \,(314t+\pi /3)\]

D)

None of these

View Solution

57)

In a LCR circuit capacitance is changed from C to 1C. For the resonant frequency to remain unchanged, the inductance should be change from L to

A)

4L

B)

2L

C)

\[L/2\]

D)

\[L/4\]

View Solution

58)

As shown in figure, value of inductive reactance \[{{X}_{L}}\] will be if source voltage is 100 volt

A)

\[40\,\Omega \]

B)

\[30\,\Omega \]

C)

\[50\,\Omega \]

D)

can have any value

View Solution

59)

In a series L-C-R circuit, \[C={{10}^{-11}}\] Farad, \[L={{10}^{-5}}\] Henry and R=100 Ohm, when a constant D.C. voltage E is applied to the circuit, the capacitor acquires a charge \[{{10}^{-9}}\,C\]. The D.C. source is replaced by a sinusoidal voltage source in which the peak voltage \[{{E}_{0}}\]is equal to the constant D.C. voltage E. At resonance the peak value of the charge acquired by the capacitor will be:

A)

\[{{10}^{-15}}\,C\]

B)

\[{{10}^{-6}}\,C\]

C)

\[{{10}^{-10}}\,C\]

D)

\[{{10}^{-8}}\,C\]

View Solution

60)

In a uniform magnetic field of induction B a wire in the form of a semicircle of radius r rotates about the diameter of the circle with an angular frequency \[\omega \]. The axis of rotation is perpendicular to the field. If the total resistance of the circuit is R, the mean power generated per period of rotation is

A)

\[\frac{{{(B\pi r\omega )}^{2}}}{2R}\]

B)

\[\frac{{{(B\pi {{r}^{2}}\omega )}^{2}}}{8R}\]

C)

\[\frac{B\pi {{r}^{2}}\omega }{2R}\]

D)

\[\frac{{{(B\pi r{{\omega }^{2}})}^{2}}}{8R}\]

View Solution

61)

An ac source of angular frequency co is fed across a resistor R and a capacitor C in series. The current registered is I. If now the frequency of source is changed to \[\omega /3\] (but maintaining the same voltage), the current in the circuit is found to be halved. Then the ratio of reactance to resistance at the original frequency \[\omega \]is

A)

\[\sqrt{3/5}\]

B)

\[\sqrt{5/3}\]

C)

\[\sqrt{2/3}\]

D)

\[\sqrt{3/2}\]

View Solution

62)

In the LC circuit, the current is in the direction shown and the charges on the capacitor plates have the signs shown. At this time,

A)

I is increasing and Q is increasing

B)

I is increasing and Q is decreasing

C)

I is decreasing and Q is increasing

D)

I is decreasing and Q is decreasing

View Solution

63)

An LCR circuit contains resistance of 100 ohm and a supply of 200 volt at 300 radian angular frequency If only capacitance is taken out from the circuit and the rest of the circuit is joined, current lags behind the voltage by \[60{}^\circ \].If on the other hand, only inductor is taken out, the current leads by \[60{}^\circ \]with the applied voltage. The current flowing in the circuit is:

A)

1 A

B)

1.5 A

C)

2 A

D)

2.5 A

View Solution

64)

In an electrical circuit R, L, C and an a.c. voltage source are all connected in series. When L is removed from the circuit, the phase difference between the voltage the current in the circuit is\[\pi /3\]. If instead, C is removed from the circuit, the phase difference is again \[\pi /3\]. The power factor of the circuit is :

A)

\[1/2\]

B)

\[1/\sqrt{2}\]

C)

1

D)

\[\sqrt{3}/2\]

View Solution

65)

In given RC circuit, capacitance of capacitor \[{{C}_{1}}=3\mu F\]and \[{{C}_{2}}=1\mu F\]. It is given that time constant of circuit between A and B is 3 millisecond. Value of R will be

A)

\[1\,\Omega \]

B)

\[10\,\Omega \]

C)

\[100\,\Omega \]

D)

\[1000\,\Omega \]

View Solution

66)

The circuit shown has been operating for a long time. The instant after the switch in the circuit labeled S is opened, what is the voltage across the inductor \[{{V}_{L}}\] and which labeled point (A or B) of the inductor is at a higher potential? Take \[{{R}_{1}}=4.0\,\Omega \], \[{{R}_{2}}=8.0\,\Omega \] and \[L=2.5\,H\].

A)

\[{{V}_{L}}=12V\], point A is at the higher potential

B)

\[{{V}_{L}}=12V\], point B is at the higher potential

C)

\[{{V}_{L}}=6V\], point A is at the higher potential

D)

\[{{V}_{L}}=6V\], point B is at the higher potential

View Solution

67)

In the circuit shown below, the key K is closed at t=0. The current through the battery is

A)

\[\frac{V{{R}_{1}}{{R}_{2}}}{\sqrt{R_{1}^{2}+R_{2}^{2}}}\] at t=0 and \[\frac{V}{{{R}_{2}}}\] at \[t=\infty \]

B)

\[\frac{V}{{{R}_{2}}}\] at t=0 and \[\frac{V({{R}_{1}}+{{R}_{2}})}{{{R}_{1}}{{R}_{2}}}\] at \[t=\infty \]

C)

\[\frac{V}{{{R}_{2}}}\] at t=0 and \[\frac{V{{R}_{1}}{{R}_{2}}}{\sqrt{R_{1}^{2}+R_{2}^{2}}}\] at \[t=\infty \]

D)

\[\frac{V({{R}_{1}}+{{R}_{2}})}{{{R}_{1}}{{R}_{2}}}\] at t=0 and \[\frac{V}{{{R}_{2}}}\] at \[t=\infty \]

View Solution

68)

An arc lamp requires a direct current of 10 A at 80 V to function. If it is connected to a 220 V (rms),50 Hz AC supply, the series inductor needed for it to work is close to :

A)

0.044 H

B)

0.065 H

C)

80 H

D)

0.08 H

View Solution

69)

In a series LCR circuit \[R=200\Omega \] and the voltage and the frequency of the main supply is 220V and 50 Hz respectively. On taking out the capacitance from the circuit the current lags behind the voltage by \[30{}^\circ \]. On taking out the inductor from the circuit the current leads the voltage by \[30{}^\circ \]. The power dissipated in the LCR circuit is

A)

305 W

B)

210W

C)

Zero W

D)

242 W

View Solution

70)

A fully charged capacitor C with initial charge \[{{q}_{0}}\] is connected to a coil of self-inductance L at\[t=0.\]The time at which the energy is stored equally between the electric and the magnetic fields is:

A)

\[\frac{\pi }{4}\sqrt{LC}\]

B)

\[2\pi \sqrt{LC}\]

C)

\[\sqrt{LC}\]

D)

\[\pi \sqrt{LC}\]

View Solution

71)

An inductor (L=0.03 H) and a resistor\[(R=0.15k\Omega )\]are connected in series to a battery of 15V emf in a circuit shown below. The key \[{{K}_{1}}\] has been kept closed for a long time. Then at t= 0, \[{{K}_{1}}\] is opened and key \[{{K}_{2}}\], is closed simultaneously. At f = 1 ms, the current in the circuit will be : \[({{e}^{5}}\cong 150)\]

A)

6.7 Ma

B)

0.67 mA

C)

100 mA

D)

67 mA

View Solution

72)

A resistor 'R' and \[2\mu F\] capacitor in series is connected through a switch to 200 V direct supply. Across the capacitor is a neon bulb that lights up at 120 V. Calculate the value of R to make the bulb light up 5 s after the switch has been closed, \[(lo{{g}_{10}}2.5=0.4)\]

A)

\[1.7\times {{10}^{5}}\Omega \]

B)

\[2.7\times {{10}^{6}}\Omega \]

C)

\[3.3\times {{10}^{7}}\Omega \]

D)

\[1.3\times {{10}^{4}}\,\Omega \]

View Solution

73)

In the circuit shown here, the point 'C' is kept connected to point 'A' till the current flowing through the circuit becomes constant. Afterward, suddenly, point 'C' is disconnected from point 'A' and connected to point 'B' at time t=0. Ratio of the voltage across resistance and the inductor at t = L/R will be equal to:

A)

\[\frac{e}{1-e}\]

B)

1

C)

- 1

D)

\[\frac{1-e}{e}\]

View Solution

74)

Combination of two identical capacitors, a resistor R and a dc voltage source of voltage 6V is used in an experiment on a (C-R) circuit. It is found that for a parallel combination of the capacitor the time in which the voltage of the fully charged combination reduces to half its original voltage is 10 second. For series combination the time needed for reducing the voltage of the fully charged series combination by half is

A)

10 second

B)

5 second

C)

2.5 second

D)

20 second

View Solution

75)

In an LCR circuit as shown below both switches are open initially. Now switch\[{{S}_{1}}\]is closed, \[{{S}_{2}}\] kept open. (q is charge on the capacitor and\[\tau =RC\]is Capacitive time constant). Which of the following statements is correct?

A)

At, t=0, q=CV (1-e)

B)

At,\[t=\tau \], \[q=CV/2\]

C)

At, \[t=2\tau \], \[q=CV(1-{{e}^{-e}})\]

D)

At, \[t=2\tau \], \[q=CV(1-{{e}^{-1}})\]

View Solution

76)

Figure shows an iron - cored transformer assumed to be 100% efficient. The ratio olf the secondary turns to the primary turns is 1:20.

A 240 V ac supply is connected to the primary coil and a 6 W resistor is corrected to the secondary coil. What is the current in the primary coil?

A)

0.10 A

B)

0.14 A

C)

2 A

D)

40 A

View Solution

77)

A step down transformer is connected to 2400 volts line and 80 amperes of current is found to flow in output load. The ratio of the turns in primary and secondary coil is 20:1. If transformer efficiency is 100%, then the current flowing in the primary coil will be

A)

1600 amp

B)

20 amp

C)

4 amp

D)

1.5 amp

View Solution

78)

At t < 0, the capacitor is charged and the switch is opened. At t=0 the switch is closed. The shortest time T at which the charge on the capacitor will be zero is given by

A)

\[\pi \sqrt{LC}\]

B)

\[\frac{3}{2}\pi \sqrt{LC}\,\]

C)

\[\frac{\pi }{2}\sqrt{LC}\,\]

D)

\[2\pi \sqrt{LC}\,\]

View Solution

79)

The primary and secondary coil of a transformer have 50 and 1500 turns respectively. If the magnetic flux \[\phi \] linked with the primary coil is given by \[\phi ={{\phi }_{0}}+4t\], where \[\phi \] is in webers, t is time in seconds and \[{{\phi }_{0}}\] is a constant, the output voltage across the secondary con is

A)

120 volts

B)

220 volts

C)

30 volts

D)

90 volts

View Solution

80)

An ideal efficient transformer has a primary power input of 10 kW. The secondary current when the transformer is on load is 25 A. If the primary: secondary turns ratio is 8 : 1, then the potential difference applied to the primary coil is

A)

\[\frac{{{10}^{4}}\times {{8}^{2}}}{25}V\]

B)

\[\frac{{{10}^{4}}\times 8}{25}V\]

C)

\[\frac{{{10}^{4}}}{25\times 8}V\]

D)

\[\frac{{{10}^{4}}}{25\times {{8}^{2}}}V\]

View Solution

81)

A transformer is used to light a 140 W, 24 V bulb from a 240 V a.c. mains. The current in the main cable is 0.7 A. The efficiency of the transformer is

A)

\[63.8\text{ }%\]

B)

\[83.3\text{ }%\]

C)

\[16.7%\]

D)

\[36.2%\]

View Solution

82)

In an ideal transformer, the voltage and the current in the primary coil are 200 V and 2 A, respectively. If the voltage in the secondary coil is 2000 V, the value of current in the secondary coil will be

A)

0.2 A

B)

2 A

C)

10 A

D)

20 A

View Solution

83)

In an oscillating LC circuit with L = 50 mH and\[C=4.0\,\mu F\], the current is initially a maximum. How long will it take before the capacitor is fully discharged for the first time:

A)

\[7\times {{10}^{-4}}\,s\]

B)

\[14\times {{10}^{-4}}\,s\]

C)

\[28\times {{10}^{-4}}\,s\]

D)

none of these

View Solution

84)

The primary of a winding transformer has 400 turns while the secondary has 2000 turns. If the power output from the secondary at 1000 V is 12 kW, what is the primary voltage?

A)

200V

B)

300V

C)

400V

D)

500V

View Solution

85)

Figure shows three oscillating LC circuit with identical inductors and capacitors. If\[{{t}_{1}}\], \[{{t}_{2}}\], \[{{t}_{3}}\] are the time taken by the circuits I, II, III for fully discharge, then

A)

\[{{t}_{1}}>{{t}_{2}}>{{t}_{3}}\]

B)

\[{{t}_{1}}<{{t}_{2}}<{{t}_{3}}\]

C)

\[{{t}_{2}}<{{t}_{1}}<{{t}_{3}}\]

D)

\[{{t}_{3}}=\sqrt{{{t}_{1}}{{t}_{2}}}\]

View Solution

86)

The primary of a transformer when connected to a dc battery of 10 volt draws a current of 1 mA. The I number of turns of the primary and secondary windings are 50 and 100 respectively The voltage in the secondary and the current drawn by the circuit in the secondary are respectively

A)

20 V and 0.5 mA

B)

20 V and 2.0 mA

C)

10 V and 0.5 mA

D)

Zero and therefore no current

View Solution

87)

A transformer having efficiency of 90% is working on 200V and 3kW power supply. If the current in the secondary coil is 6A, the voltage across the secondary coil and the current in the primary coil respectively are:

A)

300V, 15A

B)

450V, 15A

C)

450V, 13.5A

D)

600V, 15A

View Solution

88)

For long distance transmission, the A.C.is stepped up because of high voltage, the transmission is

A)

faster

B)

economical

C)

undamped

D)

less dangerous

View Solution

89)

A capacitor in an LC oscillator has a maximum potential difference of 17 V and a maximum energy of \[160\,\mu J\]. When the capacitor has a potential difference of 5V and an energy of \[10\,\mu J,\] what is the energy stored in the magnetic field?

A)

\[10\,\mu J\]

B)

\[150\,\mu J\]

C)

\[160\,\mu J\]

D)

\[170\,\mu J\]

View Solution

90)

A transformer rated at 10 KW is used to connect a 5 KV transmission line to a 240V circuit. The ratio of turns in the windings of the transformer is:

A)

5

B)

20.8

C)

104

D)

40

View Solution

91)

A step up transformer operates on a 230 V line and supplies a current of 2 ampere. The ratio of primary and secondary winding is 1:25. The current in primary is

A)

25 A

B)

50 A

C)

15 A

D)

12.5 A

View Solution

92)

The tuning circuit of a radio receiver has a resistance of \[50\,\Omega \], an inductor of 10 mH and a variable capacitor. A 1 MHz radio wave produces a potential difference of 0.1 mV. The values of the capacitor to produce resonance is \[(Take\,{{\pi }^{2}}=10)\]

A)

2.5 pF

B)

5.0 pF

C)

25 pF

D)

50 pF

View Solution

93)

A generator at a utility company produces 100 A of current at 4000 V. The voltage is stepped up to 2, 40, 000V by a transformer before it is sent on a high voltage transmission line. The current in transmission line is

A)

3.67 A

B)

2.67 A

C)

1.67 A

D)

2.40 A

View Solution

94)

A transistor-oscillator using a resonant circuit with an inductor L (of negligible resistance) and a capacitor C in series produce oscillations of frequency f. If L is doubled and C is changed to 4C, the frequency will be

A)

\[8f\]

B)

\[f/2\sqrt{2}\]

C)

\[f/2\]

D)

\[f/4\]

View Solution

95)

A 220 volts input is supplied to a transformer. The output circuit draws a current of 2.0 ampere at 440 volts. If the efficiency of the transformer is 80%, the current drawn by the primary windings of the transformer is

A)

3.6 ampere

B)

2.8 ampere

C)

2.5 ampere

D)

5.0 ampere

View Solution

JEE Main & Advanced Physics Alternating Current / प्रत्यावर्ती धारा Question Bank

done Self Evaluation Test - Alternating Current Total Questions - 95

Study Package

Self Evaluation Test - Alternating Current

Self Evaluation Test - Alternating Current Total Questions - 95