Question

In a series $LCR$ circuit, the voltage across resistance, capacitance and inductance is $10 \, V$ each. If the capacitor is removed, the voltage across the inductance will be

• A. $10 \, V$
• B. $10\sqrt{2} \, V$
• C. $\frac{10}{\sqrt{2}}V$
• D. $20 \, V$

Answer 1

Answer: (C)

Given, $V_{R}=V_{L}=V_{C}=10V$
This means the LCR circuit is in resonance and the reactance of inductor and capacitor is equal to the resistance of the resistor.
$\Rightarrow V_{s u p p l y}=V_{R}=10 \, V$
After removing capacitor
$V_{s u p p l y}=\sqrt{V_{R}^{2} + V_{L}^{2}}$
Since, $V_{R}=V_{L}$
$\Rightarrow 10=\sqrt{V_{L}^{2} + V_{L}^{2}}$
$\Rightarrow 2V_{L}^{2}=100$
$V_{L}=\frac{10}{\sqrt{2}} \, V$