Correct Answer

Concept & PrincipleElectricalBasic Electrical

Option D

$90°$

Quick Summary: In a pure inductive circuit, the current lags behind the voltage by an angle of $90^\circ$ (or $\frac{\pi}{2}$ radians). This occurs because the induced back-EMF opposes the change in current, forcing the current waveform to reach its peak later than the voltage.

💡 Explanation

In a pure inductive circuit, the current lags behind the voltage by an angle of $90°$ (or $\frac{\pi}{2}$ radians). This occurs because the induced back-EMF opposes the change in current, forcing the current waveform to reach its peak later than the voltage.

🔢 Key Formulas

$v_L = L \frac{di}{dt}$ — Instantaneous voltage across an inductor

$X_L = 2\pi f L$ — Inductive reactance in Ohms

$\phi = 90°$ — Phase shift in a pure inductor

⚙️ Working Principle

According to Faraday's Law, the induced voltage across an inductor is given by $v(t) = L \frac{di}{dt}$ . For a sinusoidal current $i(t) = I_m \sin(\omega t)$ , the resulting voltage is $v(t) = \omega L I_m \sin(\omega t + 90°)$ . Thus, the phase difference $\phi$ between voltage and current is exactly $90°$ , confirming that the inductor is a purely reactive element that does not dissipate real power.

📌 Key Points

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A pure inductor has zero resistance and zero conductance.
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The power factor of a purely inductive circuit is zero lagging.
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Inductors store energy in the form of a magnetic field.
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Real inductors always contain a small amount of internal series resistance ( $R$ ).

✅ Advantages

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Inductors can be used as filters to block high-frequency noise.
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Useful for energy storage in magnetic fields for power electronics converters.

❌ Disadvantages / Limitations

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Purely inductive circuits are theoretical; real inductors have parasitic resistance.
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High inductive loads can cause voltage spikes during switching.

🛠️ Applications / Uses

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Tuned circuits and oscillators in radio frequency communication.
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Chokes for smoothing current in DC power supplies.

📄 Additional Information

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At $90°$ phase shift, the average power consumption $P = VI \cos(90°) = 0$ Watts.
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Option A is 0, which corresponds to a purely resistive circuit.
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Options B and C represent RL circuits where $R > 0$ .

📊 Diagram / Illustration

✅

D is correct — In a purely inductive circuit, the back-EMF created by the changing magnetic flux causes the current to lag the voltage by exactly $90°$ .

Core Concepts Used

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Inductive Reactance Phase Difference Lenz's Law

💡 EXAM TIP

Remember 'ELI' for inductors: In an Inductor (L), Current (I) comes after Voltage (E).

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