Question

The voltage across a device and the current through it are:

v(t)=5cos2t V i(t)=10(1-e^-0.5t)A

a. Calculate the total charge in the device at t=1 s
b. Calculate the power consumed by the device at t= 1 s

Answer 1

attached below

Step-by-step explanation:

Answer 2

Answer: Charge, Q= 22.131 columbs

Power, P = 196.65 Watts

Step-by-step explanation:

I(t) = 10( 1 - e(-0.5t)) A

I = dQ/dt

dQ = 10( 1 - e(-0.5t))dt

Integrating we have

Q = 10t - (20/(-0.5))e(-0.5t)

taking the value of t at 1s

we have,

Q = 10 + 20e(-0.5)

Q = 10 + 20/1.6487

Q = 10 + 12.131

Q = 22.131 Columbs

(b) Power

Power = voltage x current

Power = 5cos(2t) x 10(1 - e(-0.5t))

Power at t= 1, we substitute t=1

Power = 5cos(2) x 10(1 - e(-0.5))

Power = 5(0.9995) x 10(1 - 0.60654)

Power = 39.35 x 4.9975 = 196.65 Watts

Power = 196.65 Watts