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Time constant of an inductive circuit

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Answer & Explanation
Correct AnswerA. increases with the increase of inductance and the decrease of resistance

Quick Explanation

For an RL circuit the time constant is τ=L/R. It increases when inductance increases and when resistance decreases, because larger L resists current change while larger R dissipates energy faster.

Formula / Key Relation

τ = L/R
i(t) = Ifinal + [I(0⁺)−Ifinal]e^(−t/τ)

Detailed Explanation

Concept & Reasoning

After a DC step, current in a simple series RL circuit approaches its final value exponentially with time constant L/R. Roughly 63.2% of the total current change occurs after one time constant and more than 99% after about five time constants.

How to Solve It in the Exam

L upstairs, R downstairs.

Important Exam Point

Use the Thevenin resistance seen by the inductor for more general first-order networks.

Related Revision Path

This question sits in the revision path Signals and Systems → First-Order Circuits → RL Transients .

RL Time Constant explanatory diagram

Quick Trick

L upstairs, R downstairs.

Common Mistake

Writing τ=R/L, which has units of inverse seconds rather than seconds.

Exam Tip

Use the Thevenin resistance seen by the inductor for more general first-order networks.

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Previous Exam Appearances

Assistant Engineer (Electrical), Class-2, Road and Building Department2025Q. 186
Assistant Engineer (Electrical), Class-2, Road and Building Department2025Q. 186
Assistant Engineer (Electrical), Class-2, Road and Building Department2025Q. 186
Assistant Engineer (Electrical), Class-2, Road and Building Department2025Q. 186
Assistant Engineer (Electrical), Class-2, Road and Building Department2025Q. 186
Assistant Engineer (Electrical), Class-2, Road and Building Department2025Q. 186
Assistant Engineer (Electrical), Class-2, Road and Building Department2025Q. 186
Assistant Engineer (Electrical), Class-2, Road and Building Department2025Q. 186
Assistant Engineer (Electrical), Class-2, Road and Building Department2025Q. 186
Assistant Engineer (Electrical), Class-2, Road and Building Department2025Q. 186

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