Question

In a series $LCR$ circuit $R = 300 \,\Omega$, $L = 0.9H$, $C = 2\mu F$, $\omega = 1000\, rad/s$. The impedance of the circuit is

• A. $500 \,\Omega$
• B. $1300 \,\Omega$
• C. $400 \,\Omega$
• D. $900 \,\Omega$

Answer 1

Answer: (A)

Key Idea Impedance for series LCR circuit is given by
$Z=\sqrt{R^{2}+ \left(\omega L-\frac{1}{\omega C}\right)^{2}}$
Given, resistance, $R=300 \Omega$, inductance,
$L=0.9 H ,$ capacitance, $C=2 \mu F =2 \times 10^{-6} F$
and angular frequency, $\omega=1000 rad / s$.
Substituting the given values in the above equation, we get
$\Rightarrow Z=\sqrt{300^{2}+\left(1000 \times 0.9-\frac{1}{1000 \times 2 \times 10^{-6}}\right)^{2}}$
$\Rightarrow Z=\sqrt{90000+(900-500)^{2}}$
$\Rightarrow Z=\sqrt{250000}=500 \Omega$
Hence, the impedance of LCR circuit is $500 \Omega$