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: Understanding the Concept:
In a series LCR circuit, the voltage across the resistor is in phase with the current. The voltage across the inductor leads by 90 degrees, and the voltage across the capacitor lags by 90 degrees. So \(V_L\) and \(V_C\) point in opposite directions and partly cancel.

Step 2: Key Formula or Approach:
\[ V = \sqrt{V_R^2 + (V_L - V_C)^2} \]

Step 3: Detailed Explanation:
\[ V = \sqrt{40^2 + (60 - 30)^2} = \sqrt{1600 + 900} = \sqrt{2500} = 50 \text{ V} \]
Option (D) 130 V simply adds all three voltages, which ignores the phase differences. Option (C) 70 V adds \(V_R\) and \(V_L - V_C\) directly, and option (A) 10 V is not obtained by any correct combination.

Final Answer:
The supply voltage is 50 V, option (B). \[ \boxed{50 \text{ V (B)}} \]