Question

A 100 volt A.C. source of frequency 500 hertz is connected to a L-C-R circuit with L $=$ 8.1 millihenry, C $=$ 12.5 microfarad and R $=$ 10 ohm, all connected in series. The potential difference across the resistance will be:

• A. 10V
• B. 100V
• C. 50V
• D. 500V

Answer 1

Answer: (B)

100V

Impedance of series RLC circuit is given by:

$Z=\sqrt{R^2+{(2\pi fL-\frac{1}{2\pi fC})}^2}$

$Z=\sqrt{{10}^2+{(2\pi \times 500\times 8.1\times {10}^{-3}-\frac{1}{2\pi \times 500\times 12.5\times {10}^{-6}})}^2}$

$Z\approx 10\Omega$

Current flowing through the circuit is:

$I=\frac{V}{Z}=10A$

Potential difference across the resistor, by ohm's Law is:

$V_R=IR=10\times 10=100V$