Question

Find the power delivered to an element at t=3ms of current entering its positive terminal is i=10cos50πt a and the voltage is v=64 di/dt

Answer 1

Power delivered is given by equation

$P = V*i$

given that

$V = 64\frac{di}{dt}$

$i = 10 cos50\pi t$

now plug in all values above

$P = 64\frac{di}{dt}* 10 cos50\pi t$

plug in value of current in above equation

$P = 64*\frac{d}{dt}(10cos50\pi t}* 10cos50\pi t$

$P = 64* (10*50\pi* sin50\pi t)* 10cos50\pi t$

at t = 3 ms

$P = 64* 500\pi * sin(50 \pi* 0.003) * 10 cos(50\pi * 0.003)$

$P = 1.3*10^5 Watt$

so the power is given by above value at the given instant of time