An RL circuit is excited by a DC step voltage. Then1.Initial current through inductor is zero.2.Final current depends only on resistance.3.Time constant depends only on inductance.4.Current rises exponentially with time.Which of the above statements is/are correct?

Correct Answer: C - 1, 2 and 4 only

Quick Concept Explanation

In a first-order RL circuit driven by a DC step, inductor current cannot change instantaneously. The time constant depends on both inductance and resistance, so changing either alters the transient speed. Key relation: i(t)=V/R·(1−e^(−t/τ)); τ=L/R.

Exam focus: Initial inductor current is continuous; final DC inductor acts as a short circuit. Common trap: Do not write τ=L alone; resistance is part of the time constant.

Statement-wise Verification

• Statement 1 - Correct.
  Initial current through inductor is zero.
  Initial inductor current is continuous; final DC inductor acts as a short circuit.
• Statement 2 - Correct.
  Final current depends only on resistance.
  Initial inductor current is continuous; final DC inductor acts as a short circuit.
• Statement 3 - Incorrect.
  Time constant depends only on inductance.
  For a simple RL circuit τ=L/R, so resistance and inductance both matter
• Statement 4 - Correct.
  Current rises exponentially with time.
  Starting from zero current, it rises exponentially toward the steady value V/R.

Core Concept

In a first-order RL circuit driven by a DC step, inductor current cannot change instantaneously. Starting from zero current, it rises exponentially toward the steady value V/R. The time constant depends on both inductance and resistance, so changing either alters the transient speed.

Formula / Key Relationship

i(t)=V/R·(1−e^(−t/τ)); τ=L/R.

Why the Other Options Are Wrong

Option A is incorrect because it omits correct statement(s) 2. Option B is incorrect because it includes incorrect statement(s) 3 and omits correct statement(s) 2, 4. Option D is incorrect because it includes incorrect statement(s) 3.

Exam Shortcut / Approach

Initial inductor current is continuous; final DC inductor acts as a short circuit.

Common Mistake

Do not write τ=L alone; resistance is part of the time constant.

Quick Revision

RL Step Response is linked with First-Order RL Circuit, Transient Analysis and Network Theory. Initial inductor current is continuous; final DC inductor acts as a short circuit.