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 $X_{C}=\frac{1}{\omega C}$
$=\frac{1}{7 0\times 10^{3} \times 1 \times 1 0=-6}$
$=\frac{10^{3}}{70}=\frac{1000}{70}$
$=14.3$
Hence, $X_{C} >X_{L}$
Therefore, the circuit will be R-C circuit.