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A series L-C-R circuit with R = 20 Omega...

A series L-C-R circuit with R = `20 Omega`, L = 1.5 H and C =` 35muF` is connected to a variable frequency 200 V, AC supply. When the frequency of the supply equals the natural frequency of the circuit, what is the average power transfered to the circuit, what is the average power transfered to the circuit in one complete cycle ?

Text Solution

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When the frequency of the supply equals the natural frequeny of the circuit, the circuit is said to be in resonance.
At resonance,
? Z=R = `20Omega`
Since, the L-C-R circuit is resistive, so the phase angle between the current and voltage is zero.
i.e. `phi = 0^(2)` and `I_(rms) = (E_(rms))/Z = 200/10 = 10A`
P=Average power transffered per cycle.
`therefore P=I_(rms)E_(rms)cos0^(@)`
`=10 xx 200 = 2000 W = 2.0 kW`
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