A current with sinusoidal time-dependence, whose peak value is 6.55 A and freque

Question

A current with sinusoidal time-dependence, whose peak value is 6.55 A and frequency is 775 cycles per second, passes through a long straight wire. A rectangular 27.2 cm × 12.2 cm loop of copper wire is located 30.2 cm from the wire and is coplanar with it. Calculate the average power dissipated by the loop, if its resistance is 94.3 ?.

sapling learning A current with sinusoidal time-dependence, whose peak value s 6.55 A and frequency is 775 cycles per second, passes through a long straight wire. A rectangular 27.2 cm x12.2 cm loop of copper wire is located 30.2 cm from the wire and is coplanar with it. Calculate the average power dissipated by the loop, if its resistance is 94.3 2. Number 30.2 cm 12.2 cm 27.2 cm

Explanation / Answer

magnetic field B = uo I /( 2pi x)

magnetic flux phi = B A

Phi = (u0 I)/2 pi x) * (0.122 dx)

emf e = dphi/dt = (2*10^-7 *6.55* 775* cos (775 rad) * 0.122 * ln ( 0.574/0.302)

emf = 7.95 *10^-7 cos wt

induced current I = emf/R

I = 7.95 *10^-7 * 2*3.14* 775 * cos wt /94.3

I = 4.1 *10^-5 Cos wt

Avg Power P = I^2R cos wt

P = 4.1 *10^-5 * 4.1*10^-5 * 94.3

P = 1.58 *10^-7 watts

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