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3 February, 07:04

In an electromagnetics lab, you are studying two coils which have a mutual inductance of M=300 mH. Suppose that the current in the 1st coil increased linearly from 2.8 A to 10 A in a span of 300 ms and that the 2nd coil has a resistance of R=0.4 Ohm, what is the magnitude of the induced current I in the 2nd coil? (Note: write only the two digits in the space provided for value of current in amperes).

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  1. 3 February, 07:16
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    Given that,

    The mutual inductance of the two coils is

    M = 300mH = 300 * 10^-3 H

    M = 0.3 H

    Current increase in the coil from 2.8A to 10A

    ∆I = I_2 - I_1 = 10 - 2.8

    ∆I = 7.2 A

    Within the time 300ms

    t = 300ms = 300 * 10^-3

    t = 0.3s

    Second Coil resistance

    R_2 = 0.4 ohms

    We want to find the current in the second coil,

    The same induced EMF is in both coils, so let find the EMF,

    From faradays law

    ε = Mdi/dt

    ε = M•∆I / ∆t

    ε = 0.3 * 7.2 / 0.3

    ε = 7.2 Volts

    Now, this is the voltage across both coils,

    Applying ohms law to the second coil, V=IR

    ε = I_2•R_2

    0.72 = I_2 • 0.4

    I_2 = 0.72 / 0.4

    I_2 = 1.8 Amps

    The current in the second coil is 1.8A
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