First slide

Alternating Current and voltage

Question

In a region of uniform magnetic induction $B = 10^{- 2} tesla$ , a circular coil of radius 30 cm and resistance $π$ ² ohm is rotated about an axis which is perpendicular to the direction of B and which forms a diameter of the coil. If the coil rotates at 200 rpm the amplitude of the alternating current induced in the coil is

Moderate

A

4 $π$ ² mA
B

30 mA
C

6 mA
D

200 mA

Solution

Amplitude of $ac = i_{0} = \frac{V_{0}}{R} = \frac{ωNBA}{R} = \frac{(2 πν) NB ({πr}^{2})}{R}$
$\Rightarrow i_{0} = \frac{2 π \times \frac{200}{60} \times 1 \times 10^{- 2} \times π \times {(0 .3)}^{2}}{π^{2}} = 6 mA$

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