Question

In a series $LCR$ circuit $R=300\Omega$, $L=0.9H$, $C=2\mu F$, $\omega =1000rad/s$. 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,
$L=0.9H,$ capacitance, $C=2\mu F=2\times 10^{-6}F$
and angular frequency, $\omega =1000rad/s$.
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 $500\Omega$