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17 September, 08:30

The magnetic flux through each turn of a 110-turn coil is given by ΦB = 9.75 ✕ 10-3 sin (ωt), where ω is the angular speed of the coil and ΦB is in webers. At one instant, the coil is observed to be rotating at a rate of 8.70 ✕ 102 rev/min. (Assume that t is in seconds.) (a) What is the induced emf in the coil as a function of time for this angular speed? (Use the following as necessary: t. Do not use other variables, substitute numeric values. Assume that e m f is in volts. Do not include units

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  1. 17 September, 08:44
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    Given that a coil has a turns of

    N = 110 turns

    And the flux is given as function of t

    ΦB = 9.75 ✕ 10^-3 sin (ωt),

    Given that, at an instant the angular velocity is 8.70 ✕ 10² rev/min

    ω = 8.70 ✕ 10² rev/min

    Converting this to rad/sec

    1 rev = 2πrad

    Then,

    ω = 8.7 * 10² * 2π / 60

    ω = 91.11 rad/s

    Now, we want to find the induced EMF as a function of time

    EMF is given as

    ε = - NdΦB/dt

    ΦB = 9.75 ✕ 10^-3 sin (ωt),

    dΦB/dt = 9.75 * 10^-3•ω Cos (ωt)

    So,

    ε = - NdΦB/dt

    ε = - 110 * 9.75 * 10^-3•ω Cos (ωt)

    Since ω = 91.11 rad/s

    ε = - 110 * 9.75 * 10^-3 * 91.11 Cos (91.11t)

    ε = - 97.71 Cos (91.11t)

    The EMF as a function of time is

    ε = - 97.71 Cos (91.11t)

    Extra

    The maximum EMF will be when Cos (91.11t) = - 1

    Then, maximum emf = 97.71V
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