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Question

# A series LCR with R=20 Ω, 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?

A
100 Watt
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B
200 Watt
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C
1000 Watt
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D
2000 Watt
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Solution

## The correct option is D 2000 WattAverage power transferred Pavg=12I0V0cosϕ From the phasor diagram, cosϕ=RZ At resonance, XL=XC and therefore, Z=R cosϕ=1 and Pavg=12I0V0cosϕ =VrmsIrmscosϕ =VrmsIrms Given Vrms=200 V Irms=VrmsZ=VrmsR =200 V20 Ω=10 A ∴Pavg=200×10=2000 Watt

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