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Question
The mutual inductance of two coils is 10 mH. If the current in one of the coil changes from 5 A to 1 A in 0.2 s, calculate the emf induced in the other coil. Also calculate the induced charge flowing through the coil if its resistance is 5 Ω.
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Solution
Data: M = 10 mH = 10-2 H, I1i = 5 A, I1f = 1 A, Δ t = 0.2 s, R = 5 Ω
The mutually induced emf in coil 2 due to the changing current in coil 1,
`"e"_21 = - "M" (triangle "I"_1)/(triangle "t") = - "M" ("I"_(1"f") - "I"_(1"i"))/(triangle "t")`
`= - (10^-2)((1 - 5)/0.2)` = 0.2 V
If ΔQ2 is the charge that flows through coil 2 due to the changing current in coil 1, the induced current in coil 2 is
`"I"_2 = (triangle "Q"_2)/(triangle "t") = "e"_2/"R"_2`
∴ ΔQ2 = `"e"_2/"R"_2 triangle "t" = 0.2/5 (0.2) = 0.04/5`
= 0.008 C = 8 mC
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