1) 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 and increasing toward a maximum. 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 maximum current amplitude). What is the unknown element?

Capacitor

Explanation:

Given the following ;

At time, t = T/4 ; I = 0

At time, t = T/2 ; I = - Imax

Where T = period

We can confirm what the unknown element is by using the relation, such that the parameters satisfy the stated condition ;

Recall;

I = Iosin(wt + π/2) [for CAPACITOR]

w = 2π/T

At t = T/4

I = Iosin(2π/T(T/4) + π/2)

I = Iosin(π/2 + π/2)

I = Iosin(0)

I = 0

At t = T/2

I = Iosin(2π/T(T/2) + π/2)

I = Iosin(π + π/2)

I = Iosin(0)

I = Iosin(3π/2)

I = Iosin(540/2)

I = Iosin(270)

I = -Io

Note : Io = Imax

Both conditions are met, Hence, the unknown element is a CAPACITOR.

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