Question

A device X is connected across an ac source of voltage V = V0 sin ωt. The current through X is

given as I = I0 sin ( ωt + π/2).

(i) Identify the device X and write the expressions for its reactance.

(ii) Draw graphs showing the variation of voltage and current with time over one cycle of ac,

for X.

(iii) Show the variation of reactance of device X with frequency graphically.

(iv) Draw the phasor diagram for the device X.​

Answer 1

1. Device X is a capacitor because the current is leading the voltage by π/2 .

Capacitive reactance :-

$X_C \:=\: \dfrac{1}{\omega C}$

2. Graph has been attached. The Current leads the voltage by 90°.

$X_C \:=\: \dfrac{1}{\omega C} \\ \\ \\ \\ \implies X_C\:=\: \dfrac{1}{2\pi f C} \\ \\ \\ \implies X_C \times f \:=\: Constant$

3. Thus, f is inversely proportional to Capacitive reactance. That is the graph will be rectangular hyperbola. The graph is attached.

4. Device X is Capacitor. Voltage lahs the current by 90°. The phasor diagram is attached.

Additional Information

• X would have been an inductor if the current lagged voltages by π/2. That is :-

I = I(0) sin ( ωt - π/2).

In this case the reactance if the circuit is called inductive reactance and is given by :-

$X_L \:=\: \omega L$

• Had X been a resistor, the current and voltage would have been in the same phase.

Answer 2

Answer:

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