The total charge entering a terminal is given by q=5tsin4pi tmC Calculate the current at t=0.5s

Question

Answer 1

To calculate the current, we need to find the rate of change of the charge with respect to time. The current

is given by the derivative of the charge

with respect to time

.Given:

We need to find:

Using the product rule for differentiation, where

and \( v = \sin(4\pi t) \):

First, compute the derivatives:

Now apply the product rule:

Next, evaluate this derivative at

s:

Since \( \sin(2\pi) = 0 \) and \( \cos(2\pi) = 1 \):

Therefore, the current at

s is:

Soru