Question

In an LCR series circuit, the potential difference across the terminals of the inductor, capacitor and resistor is 60 V, 30 V and 40 V respectively. Then supply voltage will be equal to

• A. \(10\) V
• B. \(50\) V
• C. \(70\) V
• D. \(130\) V

Hint:

The inductor and capacitor voltages are opposite in phase, so V = sqrt(V_R^2 + (V_L - V_C)^2).

Answer 1

The Correct Option is B

Step 1: Draw the phasor triangle:
Put $V_R = 40$ V along the horizontal axis. Put $V_L = 60$ V upward and $V_C = 30$ V downward. The net vertical part is $60 - 30 = 30$ V.

Step 2: Pythagoras:
The supply voltage is the hypotenuse of a triangle with sides 40 and 30, so it is 50 V (a 3-4-5 triangle scaled by 10).

Step 3: Reject the rest:
130 V is the plain sum of the three readings, which would only hold if all three were in phase.

Final Answer:
Option (B). \[ \boxed{50 \text{ V (B)}} \]