Question

The voltage across a 5-uF capacitor is: v (t )equals 10 cos open parentheses 6000 t close parentheses space straight V. What is the current through this capacitor?

Answer 1

Answer:

- 0.3sin6000t A

Explanation:

Voltage, v = 10 cos 6000t V

Capacitance = 5-uF

Current flowing through, i(t)

i(t) = c * d/dt (V)

c = 5-uF = 5 * 10^-6 F

i(t) = (5 * 10^-6) * d/dt(10 cos 6000t)

d/dt(10 cos 6000t) = (10 * 6000) * (-sin 6000t)

Hence,

i(t) = (5*10^-6) * (10*6000) * (-sin 6000t)

i(t) = 5*10^-6 * 6*10^4 * - sin6000t

i(t) = 30 * 10^-2 * - sin6000t

i(t) = 0.3*-sin6000t

i(t) = - 0.3sin6000t Ampere