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\times10^{3}\times100\times10^{-6} $
$=7\,\Omega$
Capacitance reactance
$X_{C}=\frac{1}{\omega C}=\frac{1}{70\times10^{3}\times1\times10^{-6}}$
$=\frac{1}{70\times10^{-2}}=\frac{10^{2}}{7}=\frac{100}{7}$
As $X_{C} > X_{L}$
So, circuit behaves like $R-C $ circuit.