question_answer

The following series L-C-R circuit, when driven by an emf source of angular frequency 70 kilo-radians per second, the circuit effectively behaves like

A)  purely resistive circuit

B)  series R-L circuit

C)  series R-C circuit

D)  series L-C circuit

Correct Answer: C

Solution :

with R = 0   Here, \[\omega =70\times {{10}^{3}}rad\,{{s}^{-1}}\] Impedance of the circuit is \[Z=\sqrt{{{({{X}_{L}}\tilde{\ }{{X}_{C}})}^{2}}+{{R}^{2}}}\] If \[{{X}_{L}}>{{X}_{C}},\]then circuit is called R-L circuit. If\[{{X}_{L}}<{{X}_{C}},\]then circuit is called R-C circuit. \[\therefore \]  \[{{X}_{L}}=\omega L=70\times {{10}^{3}}\times 100\times {{10}^{-6}}\]                 \[=7\Omega \]and          \[{{X}_{C}}=\frac{1}{\omega C}=\frac{1}{70\times {{10}^{3}}\times 1\times {{10}^{-6}}}\]                 \[=\frac{{{10}^{3}}}{70}=\frac{1000}{70}=14.3\] Hence,                  \[{{X}_{C}}>{{X}_{L}}\] Therefore, the circuit will be R-C circuit.