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 with R = 0  

Correct Answer: C

Solution :

Impedance, \[Z=\sqrt{{{({{X}_{L}}\tilde{\ }{{X}_{C}})}^{2}}+{{R}^{2}}}\] or \[Z=\sqrt{{{\left( \omega L\tilde{\ }\frac{1}{\omega C} \right)}^{2}}+{{R}^{2}}}\] Inductive reactance \[{{X}_{L}}=\omega L=70\times {{10}^{3}}\times 100\times {{10}^{-6}}\] \[=7\Omega \] Capacitance reactance \[{{X}_{C}}=\frac{1}{\omega C}=\frac{1}{70\times {{10}^{3}}\times 1\times {{10}^{-6}}}\] \[=\frac{1}{7\times {{10}^{-2}}}=\frac{{{10}^{2}}}{7}=\frac{100}{7}\] As \[{{X}_{C}}>{{X}_{L}}\] Hence, circuit behave like as R-C circuit.