Question 18: AC fundamentals

Question

In a pure inductive circuit, a sinusoidal voltage $V(t)=200 \sin 250 t$ is applied to a pure inductance of $\mathrm{L}=0.02 \mathrm{H}$. The current through the coil is:

Accepted Answer

In a pure inductance L, the voltage and current satisfy
$$v(t)=L\,\frac{di}{dt}\,. $$
Here
Ã¢ÂÂ¢Ã¢ÂÂ$$v(t)=200\sin(250t)\,,\quad L=0.02m\,H$$
Ã¢ÂÂ¢Ã¢ÂÂ$$\frac{di}{dt}=\frac{200}{0.02}\sin(250t)=10^4\sin(250t)$$
Integrate:
$$i(t)=\int 10^4\sin(250t)\,dt =-\frac{10^4}{250}\cos(250t) =-40\cos(250t)\,. $$
Since
$$-\,\cos(250t)=\sin\bigl(250t-	frac{\pi}{2}\bigr),$$
we get
$$\boxed{i(t)=40\sin\Bigl(250t-	frac{\pi}{2}\Bigr)}$$
which is Option A.

Answer

$40 \sin \left[250 t-\frac{\pi}{2}\right]$

Answer

$40 \cos \left[250 t-\frac{\pi}{2}\right]$

Answer

$40 \sin \left[250 t+\frac{\pi}{2}\right]$

Answer

$40 \cos \left[250 t+\frac{\pi}{2}\right]$

AC fundamentals

In a pure inductive circuit, a sinusoidal voltage V(t)=200 \sin 250 t is applied to a pure inductance of \mathrm{L}=0.02 \mathrm{H}. The current through the coil is:

Choose the correct answer: