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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? 
  1. 100 Watt
  2. 200 Watt
  3. 1000 Watt 
  4. 2000 Watt


Solution

The correct option is D 2000 Watt
Average 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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