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A circular coil having 20 turns, each of radius 8 cm, is rotating about its vertical diameter with an angular speed of 50 `rad//s` in a uniform horizontal magnetic field of 30 mT. Obtain the maximum, average and rms value of e.m.f. induced in the coil. If the coil forms a closed loop of resistance 10 ohm, how much power is dissipated as heat |
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Answer» Here, `N = 20, r = 8 cm = 8 xx 10^(-2) m`, `omega = 50 rad s^(-1)` `B = 30 mT = 30 xx 10^(-3) T, E_(0) = ?` `E_(av) = ?, E_(v) = ?` `R = 10 Omega, P = ?` `E_(0) = N AB omega = (N pi r^(2)) B omega` `= 20 xx 3.14 xx (8 xx 10^(-2))^(2) xx 30 xx 10^(-3) xx 50` `= 0.60 V` Average value of alt. emf over full cycle, `E_(av) = 0` `E_(v) = (E_(0))/(sqrt2) = (0.60)/(1.414) = 0.42 V` Power dissipated, `P = (E_(v)^(2))/(R ) = ((0.42)^(2))/(10) = 1.76 xx 10^(-2) W` |
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