Question 255: AC fundamentals

Question

An a. c. voltage is applied to pure inductor. The current in the inductor

Accepted Answer

For a pure inductor:
The relation between voltage and current is:
$    v(t) = L \frac{di(t)}{dt}    $
If applied voltage is sinusoidal:
$    v(t) = V_m \sin(\omega t)    $
Current:
$    i(t) = \frac{1}{L} \int v(t)\,dt = \frac{1}{L} \int V_m \sin(\omega t)\,dt    $
$    i(t) = -\frac{V_m}{\omega L} \cos(\omega t) = \frac{V_m}{\omega L} \sin\left(\omega t - \frac{\pi}{2}\right)    $
Phase relation:
Current
lags
voltage by $\frac{\pi}{2}$.
Ã¢ÂÂ Correct Answer:
Option C: lags behind the voltage by $\left(\frac{\pi}{2}\right)^c$

Answer

leads the voltage by $\left(\frac{\pi}{4}\right)^c$

Answer

leads the voltage by $\left(\frac{\pi}{2}\right)^c$

Answer

lags behind the voltage by $\left(\frac{\pi}{2}\right)^c$

Answer

lags behind the voltage by $\left(\frac{3 \pi}{4}\right)^c$

AC fundamentals

An a. c. voltage is applied to pure inductor. The current in the inductor

Choose the correct answer: