The coil of an a.c. generator has 100 turns, each of cross-sectional area 2 m 2 . It is rotating at constant angular speed 30 rad / s , in a uniform magnetic field of 2 × 1 0 − 2 T . If the total resi

Question

The coil of an a.c. generator has 100 turns, each of cross-sectional area 2 m 2 . It is rotating at constant angular speed 30 rad / s , in a uniform magnetic field of 2 × 1 0 − 2 T . If the total resistance of the circuit is 600Ω then maximum power dissipated in the circuit is

TestHub · Accepted Answer

​ N = 100 , A = 2 m 2 , ω = 30 rad / s B = 2 × 1 0 − 2 T , R = 600Ω ​ Maximum power dissipated in the circuit P m a x ​ = E r m s ​ × I r m s ​ ​ = 2 ​ E 0 ​ ​ × 2 ​ I 0 ​ ​ = 2 E 0 ​ I 0 ​ ​ ... ( i ) ​ But I 0 ​ = R E 0 ​ ​ ... ( ii ) Putting (2) into (1) we get, I 0 ​ = 2 R E 0 ​ 2 ​ But E 0 ​ E 0 ​ ∴ P m a x ​ = ​ = NAB ω = 100 × 2 × 2 × 1 0 − 2 × 30 = 120 V 2 × 600 120 × 120 ​ = 12 W ​

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