Question

The amplitude of the voltage across an inductor can be greater than the amplitude of the generator EMF in an AC RLC circuit. Consider an RLC circuit with Epeak = 90 V, R = 21.1 capital omega, L = 1.05 H, and C = 2.6 µ F. Find the amplitude of the voltage across the inductor at resonance.

Answer 1

Answer:

2710.66 V

Explanation:

Eo = 90 V, R = 21.1 ohm, L = 1.05 H, C = 2.6 x 10^-6 F

At resonance, the angular frequency is given by

$\omega _{0}=\frac{1}{\sqrt{LC}}$

$\omega _{0}=\frac{1}{\sqrt{1.05\times 2.6\times 10^{-6}}}=605.23 rad/s$

XL = ω0 x L = 605.23 x 1.05 = 635.5 ohm

Xc = 1 / ω0 C = 1 / (605.23 x 2.6 x 10^-6) = 635.5 ohm

In case of resonance, the impedance is equal to teh resistance of circuit.

Z = R = 21.1 ohm

I0 = E0 / Z = 90 / 21.1 = 4.265 A

Voltage across inductor

VL = I0 x XL

VL = 4.265 x 635.5 = 2710.66 V