Q. 93.9( 21 Votes )

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

Answer :

Given:

R = 20 _{Ω}

L = 1.5 H

C = 35 μF = 35 × 10^{-6}F

Voltage supplied V = 200 V

The diagram given is:

Impedance of the circuit can be calculated as follows:

At resonance condition i.e. when ωL = 1/ωC

Z = R = 20 Ω

Current is given by the relation

I = V/R

I = 200V /20Ω

⇒ I = 10A

Therefore, the average power transferred to the circuit in one complete cycle can be calculated as follows:

Power = VI

Power = 200V × 10A

Power = 2000 W.

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Figure shows a typical circuit for low-pass filter. An AC input V_{i} = 10 mV is applied at the left end and the output V0 is received at the right end. Find the output voltages for v = 10 kHz, 100 k Hz, 1.0 MHz and 10.0 MHz Note that as the frequency is increased the output decreases and hence the name low-pass filter.

HC Verma - Concepts of Physics Part 2