Consider the following statements regarding First Order Circuits (RC):1.In an RC charging circuit, capacitor voltage increases exponentially and approaches supply voltage asymptotically.2.Time constant of an RC circuit is given by product of resistance and capacitance.3.After one time constant, capacitor voltage reaches approximately 63 percent of its final value.4.The current in RC charging circuit increases with time and reaches maximum at steady state.Which of the above statements is/are correct?

Correct Answer: A - 1, 2 and 3 only

Quick Concept Explanation

A first-order RC charging circuit responds exponentially because the capacitor voltage cannot change instantaneously. The time constant τ=RC sets the speed; at t=τ the capacitor reaches about 63.2% of its final voltage. Key relation: v_C(t)=V(1−e^(−t/RC)); i(t)=(V/R)e^(−t/RC); τ=RC.

Exam focus: One time constant = 63.2%; five time constants ≈ settled. Common trap: Charging current decreases with time; it does not increase toward steady state.

Statement-wise Verification

• Statement 1 - Correct.
  In an RC charging circuit, capacitor voltage increases exponentially and approaches supply voltage asymptotically.
  A first-order RC charging circuit responds exponentially because the capacitor voltage cannot change instantaneously.
• Statement 2 - Correct.
  Time constant of an RC circuit is given by product of resistance and capacitance.
  The time constant τ=RC sets the speed
• Statement 3 - Correct.
  After one time constant, capacitor voltage reaches approximately 63 percent of its final value.
  The time constant τ=RC sets the speed; at t=τ the capacitor reaches about 63.2% of its final voltage.
• Statement 4 - Incorrect.
  The current in RC charging circuit increases with time and reaches maximum at steady state.
  Charging current starts at V/R and decays exponentially to zero

Core Concept

A first-order RC charging circuit responds exponentially because the capacitor voltage cannot change instantaneously. Starting from zero, capacitor voltage rises toward the source and charging current decays toward zero. The time constant τ=RC sets the speed; at t=τ the capacitor reaches about 63.2% of its final voltage.

Formula / Key Relationship

v_C(t)=V(1−e^(−t/RC)); i(t)=(V/R)e^(−t/RC); τ=RC.

Why the Other Options Are Wrong

Option B is incorrect because it includes incorrect statement(s) 4 and omits correct statement(s) 2, 3. Option C is incorrect because it omits correct statement(s) 1. Option D is incorrect because it includes incorrect statement(s) 4.

Exam Shortcut / Approach

One time constant = 63.2%; five time constants ≈ settled.

Common Mistake

Charging current decreases with time; it does not increase toward steady state.

Quick Revision

RC Charging Response is linked with First-Order RC Circuit, Transient Analysis and Network Theory. One time constant = 63.2%; five time constants ≈ settled.