Question

In an LCR series circuit, if the potential differences across inductor, capacitor, and resistor are $60~\text{V}$, $30~\text{V}$, and $40~\text{V}$ respectively, then the net voltage applied to the circuit is

• A. $50~\text{V}$
• B. $70~\text{V}$
• C. $130~\text{V}$
• D. $60~\text{V}$

Hint:

Use $V = \sqrt{V_R^2 + (V_L - V_C)^2}$ in LCR circuits to get applied voltage.

Answer 1

The Correct Option is A

$V_{LC} = V_L - V_C = 60 - 30 = 30~\text{V}$
Net voltage: $V = \sqrt{V_R^2 + (V_L - V_C)^2} = \sqrt{40^2 + 30^2} = \sqrt{1600 + 900} = \sqrt{2500} = 50~\text{V}$