Question

The voltage and current across an element is given by 100e^-250t volts and 50e^-250t amperes. Calculate the energy dilivered by it (in joules) for t>=0.

Answer 1

Answer:

10 J

Explanation:

1) We have ,

$Voltage,V= 100e^{-250t} V\\ \\ Current, I=50e^{-250t} A$

Now,

$Energy,E=\int\limits^t_0 {VI} \, dt \\ \\ =>\int\limits^t_0 {100e^{-250t}*50e^{-250t}} \, dt\\ \\=>\int\limits^t_0 {5*10^3*e^{-500t}} \, dt\\ \\=>5000\int\limits^t_0 {e^{-500t}} \, dt\\ \\=>5000*\frac{e^{-500t}}{-500} \bigg\rvert_0^{\infty}\\ \\=>5000*\frac{1}{500}\\ \\=10 J$

Energy delivered by it for $t\geq 0$ is 10 Joules.