Question

A series LCR circuit is connected to a source of alternating e.m.f. of \(50\) V. The potential difference across inductor and capacitor is \(80\) V and \(50\) V respectively. The potential difference across the resistor is

• A. \(80\) V
• B. \(70\) V
• C. \(50\) V
• D. \(40\) V

Hint:

Inductor and capacitor voltages are opposite in phase and both at 90 degrees to the resistor voltage.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept
In a series LCR circuit \(V_L\) and \(V_C\) are in opposite phase and each is at \(90^{\circ}\) to \(V_R\). Source voltage \(V=\sqrt{V_R^{2}+(V_L-V_C)^{2}}\).

Step 2: Substitute
\(50^{2}=V_R^{2}+(80-50)^{2}\)
\(2500=V_R^{2}+900\)

Step 3: Solve
\(V_R^{2}=1600\), so \(V_R=40\) V.

Final Answer:
The potential difference across the resistor is 40 V. \[ \boxed{\text{(D) }40\ \text{V}} \]