Map Sapling Learning macmilan learning A 133-turn circular coil of radius 2.71 c

Question

Map Sapling Learning macmilan learning A 133-turn circular coil of radius 2.71 cm and negligible resistance is immersed in a uniform magnetic field that is perpendicular to the plane of the coil. The coil is connected to a 19.7-Q resistor to create a closed circuit. During a time interval of 0.191 s the magnetic field strength decreases uniformly from 0.555 T to zero. Find the energy, in millijoules, that is dissipated in the resistor during this time interval. Number mJ Previous O Check Answer (0 Next Exit

Explanation / Answer

we know that

EMF = -N*d(phi)/dt

phi = B.A

A = pi*r^2

i = EMF/R

So,

i = -(N*pi*r^2/R)*(dB/dt)

Using given values:

i = -(133*pi*0.0271^2/19.7)*(-0.555/0.191)

i = 0.04526 Amp.

Now

P = i^2*R

E = P*t

E = energy stored = i^2*R*dt

E = 0.04526^2*19.7*0.191

E = 0.00771 = 7.71 mJ

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