Transient analysis RL circuit/RC circuit

 Step-by-Step Guide to Solve RL/RC Transient Circuits

When studying Network Theory or preparing for competitive exams in Electrical/Electronics Engineering, one of the most important topics is Transient Analysis of RL/RC circuits. Students often get confused about how to start and what sequence of steps to follow. This article provides a simple 4-step method with examples.

🔹 What is Transient Analysis?

When a switch is operated in a circuit containing resistors (R) and inductors (L) or capacitors (C), the voltages and currents do not change instantaneously. The study of how these quantities change with time during the transition from one steady state to another is called transient analysis.

🔹 General 4-Step Method

Step 1: Find the Initial Condition (t = 0⁻)

Before switching, assume the circuit has been in steady state for a long time.

Inductor: current cannot change suddenly → 

i (0-) = i (0+)

Capacitor: voltage cannot change suddenly → 

V(0-)= V(0+)

Step 2: Calculate the Time Constant ()

Remove the energy storage element (open the capacitor / short the inductor).

Replace independent sources: voltage sources → short, current sources → open.

Find equivalent resistance .

Time constant:

For RL circuit = L/R

For RC circuit= RC

Step 3: Find the Final Value (t → ∞)

After a long time, the circuit reaches DC steady state.

Inductor → Short Circuit

Capacitor → Open Circuit

Solve for the final voltage/current of interest.

Step 4: Apply the General Solution

For any variable :

x(t) = x(∞)+ {x(0+) - x(∞)} e⁻t/τ

And て= time constant of the circuit 

Here’s a clean,  RL transient problem with a simple diagram and full solution.

Problem

At t=0 the switch S  closes, applying a DC source Vₛ =24 V to a series RL circuit with R=12 ohm , L= 60mH 

Assume zero initial current:  i (0⁻)=0

Find:

1. The current i (t)  for t>0

Solution (step-by-step)

1) Initial value (t < 0):

Switch open ⇒ no current ⇒ 

i (0-) = 0 A

2) Time constant:

τ = L/R = 0.06/12 = 5 ms

3) Final (steady-state) value (t → ∞):

i(∞) = Vₛ/R = 24/12 = 2A

4) General solution for current:

For a DC step into an RL with ,

i(t)=i(∞) + {i(0+) - i(∞) e^-t/τ

i(t) = 2 + (0 - 2) e^-t/0.005

i(t) = 2(1 - e^-t/0.005)