Question

An ac source of period T and maximum voltage V is connected to a single unknown ideal element that is either a resistor, and inductor, or a capacitor. At time t = 0 the voltage is zero. At time t = T/4 the current in the unknown element is equal to zero, and at time t = T/2 the current is I = -Imax, where Imax is the current amplitude. What is the unknown element?

Answer 1

Answer:

This satisfy the above given condition so we can say that this capacitor.

Explanation:

Let's take one by one option and check whether is wrong or right

For inductor:

$I=I_osin(wt-\frac{\pi }{2})$

Given that at t=T/4 ,I=0 and we know that

$w=\dfrac{2\pi }{T}$

So at T/4

$I=I_osin(\frac{2\pi }{T}\times \frac{T}{4}-\frac{\pi }{2})$

I=0 A

At t=T/2

$I=I_osin(\frac{2\pi }{T}\times \frac{T}{2}-\frac{\pi }{2})$

$I=I_o$

It means that this not a indutor.

For capacitor:

$I=I_osin(wt+\frac{\pi }{2})$

At T/4, I=0

At t=T/2

$I=I_osin(\frac{2\pi }{T}\times \frac{T}{2}+\frac{\pi }{2})$

$I= -I_o$

This satisfy the above given condition so we can say that this capacitor.