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Question
An inductor coil of some resistance is connected to an AC source. Which of the following quantities have zero average value over a cycle?
(a) Current
(b) Induced emf in the inductor
(c) Joule heat
(d) Magnetic energy stored in the inductor
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Solution
(a) Current
(b) Induced emf in the inductor
For a series L-R circuit, the AC current can be given by,
From the graph, we can see that the average value of current over a cycle is zero.
Since it a series L-R circuit, the phase difference between current and voltage is `pi/2`. The AC voltage can be given by,
`V = V_0 cos omega t`
From the graph, we can see that the average value of voltage over a cycle is also zero.
Joule's heat through the resistor is given by,
`H_{avg} = i_rms^2 R , "which is non zero"`
Similarly, magnetic energy stored in the inductor is given by,
`U_{avg }= 1/2 Lirms^2 , "which is also non zero" `
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