A sinusoidal voltage of peak value 250 V is applied to a series LCR circuit, in which $\mathrm{R}=8 \Omega, \mathrm{~L}=24 \mathrm{mH}$ and $\mathrm{C}=60 \mu \mathrm{F}$. The value of power dissipated at resonant condition is ' x ' kW . The value of x to the nearest integer is ____

JEE Main · 2021 · 16 Mar 2021 · Shift 1 · Alternating Current

A sinusoidal voltage of peak value 250 V is applied to a series LCR circuit, in which

R = 8Ω, L = 24 mH

and

C = 60 μ F

. The value of power dissipated at resonant condition is ' x ' kW . The value of x to the nearest integer is ____

Answer: 4

At resonance the inductive and capacitive reactances cancel, so the impedance of the series circuit is the resistance alone,

Z = R = 8 Ω

. The rms voltage across it is

V_{rms} = \frac{250}{2}

V, and the average power dissipated is

P = \frac{V _{rms}^{2}}{R} = \frac{( 250 ) ^{2}}{2 \times 8} = 3906.25 W

This is

3.906

kW, so to the nearest integer

x = 4

JEE Main · 2021 · 16 Mar 2021 · Shift 1 · Integer answer