| Directions: In the following questions, a statement of Assertion [A] is followed by a statement of Reason (R). |
| Mark the correct choice as: |
| Assertion [A]: The power in an AC circuit is minimum, if the circuit has only a resistor. |
| Reason (R): Power of a circuit is independent of the phase angle. |
A) Both Assertion [A] and Reason (R) are true and Reason (R) is the correct explanation of Assertion [A]
B) Both Assertion [A] and Reason (R) are true but Reason (R) is not the correct explanation of Assertion [A]
C) Assertion [A] is true but Reason (R) is false
D) Assertion [A] is false and Reason (R) is also false
Correct Answer: D
Solution :
(d) Power in a series AC circuit consisting of L, C and R is given by \[P={{l}_{rms}}{{V}_{rms}}\cos \phi \] where \[\phi ={{\tan }^{-1}}\left( \frac{|{{X}_{L}}-{{X}_{C}}|}{R} \right)\] For a purely resistive circuit, \[{{X}_{L}}=0\] and \[{{X}_{C}}=0\] Therefore, \[\tan \phi =0\] or \[\phi =0\] and thereby \[\cos \phi =1\] and \[P=IV\]. The power is maximum as \[\cos \phi \]is maximum. Power depends on the phase angle through the power factor \[\cos \phi \].
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