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Is it right that in LCR cicuit Power loss $=VI$ not equal to Power loss $= V²/R$?

Physics Asked on October 5, 2020

I had a doubt today (this is not my homework question, I made it up). Suppose in a LCR circuit at resonance we take out power loss as $P=VI cosphi$ (power factor and $cosphi$ becomes 1) and in another condition when there is no resonance we take out power loss as $P’= VIcosphi$ (and $cosphi = R/Z$) …..now if we divide $P/P’$ we get $R/Z$ as the result.

Now when we take different formulas for powerloss like in the resonance condition
$$P = V^2/ R $$
and in the non-resonance condition
as
$$P’ =V^2R /Z^2$$
and divide
$$P/P’ = R^2/Z^2$$
So why i am getting different results …or is there any conceptual mistake in my question ….power dissipated in both way should be the same?
I think my understanding about this is wrong. Please correct me.

One Answer

In the first case, the I at resonance is larger than when out of resonance.

Correct answer by R.W. Bird on October 5, 2020

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