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)

with $R=0$
Here, $\omega =70\times 10^{3}rad{s}^{-1}$
Impedance of the circuit is
$Z=\sqrt{{\left(X_L\sim X_C\right)}^2+R^2}$
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.