Question

A coil of resistance 10 ohm and inductance 100mH and a capacitor of variable capacitance are connected across a 20V,50Hz A.C. supply. At what capacitance will resonance occur?​

Answer 1

Given:

A coil of resistance 10 ohm and inductance 100mH and a capacitor of variable capacitance are connected across a 20V,50Hz A.C. supply.

To find:

Capacitance at which resonance will occur?

Calculation:

Resonance occurs when the Inductive Reactance and Capacitance Reactance become equal.

$\therefore \: X_{L} = X_{C}$

$\implies \: \omega L = \dfrac{1}{ \omega C}$

$\implies \: C = \dfrac{1}{ { \omega}^{2} L}$

$\implies \: C = \dfrac{1}{ {(2\pi f)}^{2} L}$

$\implies \: C = \dfrac{1}{ 4 {\pi}^{2} {f}^{2} L}$

$\implies \: C = \dfrac{1}{ 4 {\pi}^{2} \times 50 \times (100 \times {10}^{ - 3} )}$

$\implies \: C = \dfrac{1}{ 4 {\pi}^{2} \times 5}$

$\implies \: C \approx \: 0.005 \: F$

So, required capacitance is approx 0.005 F