Find the expression for the power delivered to the capacitor

Question

v(t) = 4 cos(20t) V for t > 0 and v(t) = 0 for t < 0. C1=300 uF.

Answer 1

Let Q=CV where C= 300microfarads and V=4cos(20t)V for t>0 and 0 for t<0. P=VI where I= dQ/dt. So dQ/dt = d(CV)/dt =CdV/dt. dV/dt= -80sin(20t). Therefore I= -2000sin(20t)A. Hence the power delivered to the capacitor expression is P= -8000cos(20t)sin(20t) = -4000sin(40t).