Q.
The following series $L - C - R$ circuit, when driven by an $e.m.f.$ 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 $R = 0$
Explanation
(c) Impedance, $Z = \sqrt{\left( X_{L}\sim\ X_{C} \right)^{2} + R^{2}}$
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$Z = \sqrt{\left( \omega L\sim\frac{1}{\omega C} \right)^{2} + R^{2}}$
Inductive reaction
$X_{L} = \omega L = 70 \times 10^{3} \times 100 \times 10^{- 6} = 7\Omega$
Capacitance reactance
$X_{C} = \frac{1}{\omega C} = \frac{1}{70 \times 10^{3} \times 1 \times 10^{- 6}} = \frac{100}{7}\ \ \ \left\lbrack X_{C} > X_{L} \right\rbrack$
Hence, circuit behaves like an $R$-$C$ circuit
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.