Question

A current of 4sin4t A flows through a 5-F capacitor. Find the voltage v(t) across the capacitor given that v(0)

Answer 1

Answer:

$v(t) = \frac{-cos4t}{5} + \frac{6}{5} Volts$

Explanation:

Given

current I =  4sin4t

capacitance C = 5F

v(0) = 1

The voltage across the capacitor is expressed as:

$v(t) = \frac{1}{C} \int\limits^t_{t_0} {i(t)} \, dt + v(t_0)$

Given v(0) = 1, means at t = 0, v(t0) = 1

Substitute

$v(t) = \frac{1}{5} \int\limits^t_{0} {4sin4t} \, dt + 1\\v(t) = \frac{1}{5} [\frac{-4cos4t}{4} ] + 1\\\\v(t) = \frac{1}{5} (-cos4t)+1 + \frac{1}{5}\\v(t) = \frac{-cos4t}{5} + \frac{6}{5}$