An ac source of period T and maximum voltage V is connected to a single unknown

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 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 = -I max, where I max is the current amplitude. What is the unknown element?

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

Explanation / Answer

Here ,

as initially the voltage is zero acoross the element ,

which is true in case of a initially uncharged capacitor,

as the source is AC ,

the voltage across the element changes ,

Hence , the element is d. a capacitor

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