Question

Series LCR circuit containing an a.c. source of 100V has a inductor and a capacitor of reactance \(24 \Omega\) and \(16 \Omega\) respectively. If a resistance of \(6 \Omega\) is connected in series, then the potential difference across the series combination of inductor and capacitor only is

• A. \(80\text{V}\)
• B. \(8\text{V}\)
• C. \(40\text{V}\)
• D. \(20\text{V}\)

Hint:

Find the current from the impedance, then multiply by the net reactance.

Answer 1

The Correct Option is A

Step 1: Impedance
Net reactance \(X = 24 - 16 = 8\ \Omega\). With \(R = 6\ \Omega\), \(Z = \sqrt{6^2+8^2} = 10\ \Omega\).

Step 2: Current
\(I = \frac{100}{10} = 10\ \text{A}\).

Step 3: Voltage across L and C
The combination has net reactance \(8\ \Omega\), so \(V = IX = 10\times8 = 80\ \text{V}\). Option (A).

Final Answer:
The voltage across the LC combination is 80 V. \[ \boxed{\text{(A)}\ 80\ \text{V}} \]