A series LCR-circuit with R = 20 Ω, L = 1.5 H and C = 35 μ F is connected to a variable frequency 200 V ac supply. When the frequency of the supply equals the natural frequency of the circuit, the average power transferred to the circuit in one complete cycle is

Question

A series LCR-circuit with R = 20 Ω, L = 1.5 H and C = 35 μ F is connected to a variable frequency 200 V ac supply. When the frequency of the supply equals the natural frequency of the circuit, the average power transferred to the circuit in one complete cycle is (A) 200 W (B) 2000 W (C) 100 W (D) 4000 W

Tardigrade Admin · Accepted Answer

If the frequency of the ac source equals the natural frequency of the circuit, the impedance Z=R=20 Ω The average power dissipated per cycle, Pav=(V2rms/Z) =(V2rms/R) =((200)2/20) =2000 W

Q. A series $L CR$ -circuit with $R = 20 Ω$ , $L = 1.5 H$ and $C = 35 μ F$ is connected to a variable frequency $200 V$ ac supply. When the frequency of the supply equals the natural frequency of the circuit, the average power transferred to the circuit in one complete cycle is

$200 W$

$2000 W$

$100 W$

$4000 W$

If the frequency of the ac source equals the natural frequency of the circuit, the impedance
$Z = R = 20 Ω$
The average power dissipated per cycle,
$P_{a v} = \frac{V _{r m s}^{2}}{Z}$
$= \frac{V _{r m s}^{2}}{R}$
$= \frac{( 200 ) ^{2}}{20}$
$= 2000 W$

Q. A series LCR-circuit with R=20Ω, L=1.5H and C=35μF is connected to a variable frequency 200V ac supply. When the frequency of the supply equals the natural frequency of the circuit, the average power transferred to the circuit in one complete cycle is

200W

2000W

100W

4000W