Emf applied and current in an A.C circuit are $E = 10 \sqrt{2} sin (ω t)$ $E = 10sqrt(2)sin(omegat)$ volt and $I = 5 \sqrt{2} cos (ω t)$ $I = 5sqrt(2)cos(omegat)$ ampere respectively. Average power loss in the circuit is??

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Emf applied and current in an A.C circuit are $E = 10 \sqrt{2} sin (ω t)$ $E = 10sqrt(2)sin(omegat)$ volt and $I = 5 \sqrt{2} cos (ω t)$ $I = 5sqrt(2)cos(omegat)$ ampere respectively. Average power loss in the circuit is??

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Answer 1 · 2017-08-09T15:28:33

The average power loss is zero.

Explanation:

The instantaneous power loss is, of course

$P = E I = 100 sin (ω t) cos (ω t)$ $P = EI = 100 sin(omega t) cos (omega t)$

To find the average power loss, you must integrate this over one complete period

$P_{a v} = \frac{1}{T} \int_{0}^{T} 100 sin (ω t) cos (ω t) d t$ $P_{av} = 1/T int_0^T 100 sin(omega t) cos (omega t) dt$

where $T = \frac{2 π}{ω}$ $T={2 pi}/omega$ is one time period. It is easy to see that this integral vanishes

$\int_{0}^{T} 100 sin (ω t) cos (ω t) d t$ $int_0^T 100 sin(omega t) cos (omega t) dt$
$= 50 \int_{0}^{T} sin (2 ω t) d t$ $= 50 int_0^T sin(2omega t) dt$
$= - \frac{50}{2 ω} (cos (2 ω T) - cos 0)$ $=-50/{2 omega} (cos (2omega T)-cos 0)$
$= - \frac{50}{2 ω} (cos (4 π) - cos 0) = 0$ $=-50/{2omega} (cos(4 pi) - cos 0) = 0$

Note that this is a case where the emf lags 90 degrees behind the current, as happens for a capacitor. This is an example of so called "wattles current".

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Emf applied and current in an A.C circuit are $E = 10 \sqrt{2} sin (ω t)$ $E = 10sqrt(2)sin(omegat)$ volt and $I = 5 \sqrt{2} cos (ω t)$ $I = 5sqrt(2)cos(omegat)$ ampere respectively. Average power loss in the circuit is??

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Explanation:

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Emf applied and current in an A.C circuit are E=10√2sin(ωt)E = 10sqrt(2)sin(omegat) volt and I=5√2cos(ωt)I = 5sqrt(2)cos(omegat) ampere respectively. Average power loss in the circuit is??

1 Answer

Explanation:

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Emf applied and current in an A.C circuit are $E = 10 \sqrt{2} sin (ω t)$ $E = 10sqrt(2)sin(omegat)$ volt and $I = 5 \sqrt{2} cos (ω t)$ $I = 5sqrt(2)cos(omegat)$ ampere respectively. Average power loss in the circuit is??