A rectangular coil of 20 turns and area of cross-section $$25\,sq\,cm$$ has a resistance of $$100\,\Omega .$$ If a magnetic field which is perpendicular to the plane of coil changes at a rate of $$1000\,T/s,$$ the current in the coil is
A.
$$1\,A$$
B.
$$50\,A$$
C.
$$0.5\,A$$
D.
$$5\,A$$
Answer :
$$0.5\,A$$
Solution :
Total number of tums, $$N = 20$$
Area of coil, $$A = 25\,c{m^2}$$
$$ = 25 \times {10^{ - 4}}{m^2}$$
Change in magnetic field w.r.t. $$t$$
$$\frac{{dB}}{{dt}} = 1000\,T/s$$
Resistance of coil $$R = 100\,\Omega $$
$$i = ?$$
Induced current, $$i = \frac{e}{R} = \frac{{NA\frac{{dB}}{{dt}}}}{R}\,\,\left[ {e = NA\frac{{dB}}{{dt}}} \right]$$
$$\eqalign{
& = \frac{{20 \times 25 \times {{10}^{ - 4}} \times 1000}}{{100}} \cr
& = 0.5\,A \cr} $$
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