A magnetic field given by B(t)= (0.2 t-0.05 t^2 ) T is directed perpendicular to the plane of a circular coil containing 25 turns of radius 1.8 ~cm and whose total resistance is 5 . The power dissipation at 3 ~s is nearly

Step-by-step solution

Given that, number of turns, N=25 Radius of coil, r=1.8 ~cm =1.8 10⁻² ~m Resistance of coil, R=5 Magnetic field, B= (0.2 t-0.05 t^2 ) T Now, area of coil, aligned A & = r^2=3.14 (1.8 10⁻² )^2 & =1.02 10⁻³ ~m ^2 aligned Induced emf, = -N d d t (B A)=-N A d B d t aligned & =-N A d d t (0.2 t-0.05 t^2 ) & =-N A(0.2-0.1 t) aligned Substituting the values, we get aligned & =-25 1.02 10⁻³(0.2-0.1 t) & =-2.55 10⁻²(0.2-0.1 t) aligned Now, instantaneous power, P= ^2 R = [-2.55 10⁻²(0.2-0.1 t) ]^2 5 At, t=3 ~s , power dissip