CBSE 2025, Set 3

Question

An ac source of voltage $V = V_0 \sin \omega t$ is connected to a circuit element X. It is observed that the current flowing through X varies as $I = I_0 \sin(\omega t - \frac{\pi}{2})$.
(a) Identify the element X and write the expression for its reactance.
(b) Plot a graph to show the variation of reactance of the element with the frequency of the applied voltage.
(c) Draw plots showing the variation of voltage and current with time over one cycle of applied ac.

Edvaya · Accepted Answer

The correct answer is Subjective. **(a) Identification and Reactance:**
The applied voltage is $V = V_0 \sin \omega t$.
The resulting current is $I = I_0 \sin(\omega t - \frac{\pi}{2})$.
Since the current lags the voltage by a phase angle of $\frac{\pi}{2}$ ($90^\circ$), the circuit element X is a **pure Inductor**.
The expression for its inductive reactance ($X_L$) is:
$$X_L = \omega L = 2\pi f L$$
where $f$ is the frequency and $L$ is the inductance.

**(b) Graph of Reactance vs. Frequency:**
Since $X_L = 2\pi L f$, the reactance is directly proportional to the frequency ($X_L \propto f$). The graph is a straight line passing through the origin.

![Inductive Reactance vs Frequency Graph](https://www.edvaya.com/images/cbse/physics/2025/set3/q27b-inductive-reactance-frequency-graph-answer.webp)

**(c) Plot of Voltage and Current with time:**
In an inductor, current lags voltage by $\pi/2$. When voltage is zero and rising, current is at its maximum negative value.

![Voltage and Current Time Graph](https://www.edvaya.com/images/cbse/physics/2025/set3/q27c-voltage-current-time-graph-answer.webp)

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Physics > Magnetism Induction And Alternating Current > Alternating Current

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