Question

The current through a 16-mH inductor is 4 sin 100t A.

NOTE: This is a multi-part question. Once an answer is submitted, you will be unable to return to this part.

Find the voltage v(t)
The voltage is ______ cos 100t V.

Answer 1

Using the formula for the voltage across an inductor (UL(t) = L (di/dt)), the voltage v(t) across a 16-mH inductor with a current I(t) = 4 sin 100t A is found to be 6.4 cos 100t V.

Step-by-step explanation:

The voltage v(t) across an inductor can be found using the formula UL(t) = L (di/dt), where L is the inductance and di/dt is the derivative of the current concerning time. The current given for a 16-mH inductor is I(t) = 4 sin 100t. To find the voltage, we differentiate the current concerning time:

dI/dt = 4 * 100 cos 100t = 400 cos 100t.

Then, we calculate v(t):
v(t) = L * dI/dt = 16 * 10^-3 * 400 cos 100t = 6.4 cos 100t V.

So, the voltage across the 16-mH inductor is 6.4 cos 100t V.