Question

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

Answer 1

Answer: (C)

Impedance, $Z=\sqrt{{\left(X_L\sim X_C\right)}^2+R^2}$
or $Z=\sqrt{{\left(\omega L\sim \frac{1}{\omega C}\right)}^2+R^2}$
Inductive reactance
$X_L=\omega L=70\times 10^3\times 100\times 10^{-6}$
$=7\Omega$
Capacitance reactance
$X_C=\frac{1}{\omega C}=\frac{1}{70\times 10^3\times 1\times 10^{-6}}$
$=\frac{1}{70\times 10^{-2}}=\frac{10^2}{7}=\frac{100}{7}$
As $X_C>X_L$
So, circuit behaves like $R-C$ circuit.