A current with sinusoidal time-dependence, whose peak value is 6.55 A and freque
ID: 1267674 • Letter: A
Question
A current with sinusoidal time-dependence, whose peak value is 6.55 A and frequency is 255 cycles per second, passes through a long straight wire. A rectangular 63.2 cm x 28.4 cm loop of copper wire is located 70.2 cm from the wire and is coplanar with it. Calculate the average power dissipated by the loop, if its resistance is 24.3 ohms.
The magnetic field created by the current is given by where is I0 is the peak current mu 0 = 4 pi Times 10-7 T m/A, and r is the perpendicular distance from the wire. The flux penetrating the loop of wire is The magnitude of the induced EMF is given by The power dissipated by a circuit component is which varies sinusoidally between o and a peak value of A2 omega 2/R. As noted in the hint, the time average of the power dissipated is given by Using a trigonometric identity and, therefore, find a numerical value for the average power dissipation.Explanation / Answer
the definite integral formed here is nonintegrable function and hence must be estimated
it can be estimated between 1 - T
i.e 1 < f(x) < T
where f(x) = integral(0,T) cos(wt)^2 / T dt
thus the average power lies between
6.10*10^-10 and 2.39*10^-12 W