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 10⁻² ~T . If the total resistance of the circuit is 600 then maximum power dissipated in the circuit is

Step-by-step solution

aligned & N =100, ~A =2 ~m ^2, =30 rad / s & B =2 10⁻² ~T , R =600 aligned Maximum power dissipated in the circuit aligned P_ =E_ r m s I_ r m s & = E₀ 2 I₀ 2 & = E₀ I₀ 2 ...(i) aligned But I ₀= E ₀ R ...(ii) Putting (2) into (1) we get, I ₀= E ₀ ^2 2 R aligned But E ₀ & = NAB E ₀ & =100 2 2 10⁻² 30 & =120 ~V P _ = & 120 120 2 600 =12 ~W aligned