The coil of an a.c. generator has 100 turns, each of cross sectional area `2 m^(2)`. It is rotating at a constant angular speed of 30 radians`//`s, in
The coil of an a.c. generator has 100 turns, each of cross sectional area `2 m^(2)`. It is rotating at a constant angular speed of 30 radians`//`s, in a uniform magnetic field of `2 xx 10^(-2)`T. What is the maximum power dissipated in the circuit, if the resistance of the circuit including that of the coil is `600 Omega`?
A. 6 W
B. 9 W
C. 12 W
D. 24 W
1 Answers
Correct Answer - C
`N = 1000,A = 2 m^(2), omega = 30 rad//s, T = 2 xx 10^(-2)T`,
`R = 600 Omega`
Maximum power dissipated in the circuit,
`P_(max) = E_(rms) xx I_(rms) = (E_0)/(sqrt2) xx (I_0)/(sqrt2) = (E_(0)I_(0))/(2)`
But `I_(0) = (E_0)/R`
`:. P_(max) = (E_(0) cdot E_(0))/(R xx 2) = (E_(0)^(2))/(2R) but E_(0) = NAB omega`
`:. P_(max) = ((NABomega)^(2))/(2R)`
`=((100 xx 2 xx 2 xx 10^(-2) xx 30)^(2))/(2 xx 600)`
`:. P_(max) = (120 xx 120)/(2 xx 600) = 12 W`.