Question

A sinusoidal voltage of peak value 250 V is applied to a series LCR circuit, in which R = 8 Ω, L = 24 mH, and C = 60 μF. The value of power dissipated at resonant conditions is 'x' kW.

The value of x to the nearest integer is ______.

Options

• 2

• 4

• 3

• 5

Answer 1

A sinusoidal voltage of peak value 250 V is applied to a series LCR circuit, in which R = 8 Ω, L = 24 mH, and C = 60 μF. The value of power dissipated at resonant conditions is 'x' kW. The value of x to the nearest integer is 4.

Explanation:

Peak voltage [V₀] = 250 V

So, V_RMS = `"V"_0/sqrt2 = 250/sqrt2"V"`

Resistance [R] = 8 Ω

Inductor [L] = 24 mH

Capacitor [C] = 60 µF

The dissipated power at the resonant condition

P = `(["V"_"RMS"]^2)/"R" ⇒ (250/sqrt2)^2/8`

 ⇒ 3906.25 W

Approx. P = 4 kW