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10. First-Order 
RL Circuits 
10.1
10.1 The Series RL Circuit 
10.2
10.1.1 The Series RL Circuit Equations 
10.2
10.1.2 Need for Initial Condition Specification 
10.3
10.1.3 Sufficiency of Initial Condition 
10.4
10.2 Series RL Circuit with Unit Step Input – Qualitative Analysis 
10.6
10.2.1 From t 
= 
0
-
 
to t 
= 
0
+
 
10.6
10.2.2 Inductor Current Growth Process 
10.7
10.3 Step Response of RL Circuit by Solving Differential Equation 
10.8
10.3.1 Interpreting the Input Forcing Functions in Circuit Differential Equations 10.9
10.3.2 Complementary Function and Particular Integral 
10.10
10.3.3 Series RL Circuit Response in DC Voltage Switching Problem 
10.12
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Contents
10.4 Features of RL Circuit Step Response 
10.13
10.4.1 Step Response Waveforms in Series RL Circuit 
10.15
10.4.2 The Time Constant ‘
t
’ of a Series RL Circuit 
10.16
10.4.3 Rise Time and Fall Time in First-Order Circuits 
10.17
10.4.4 Effect of Non-Zero Initial Condition on DC Switching Response
of RL Circuit 
10.18
10.4.5 Free Response of Series RL Circuit 
10.20
10.5 Steady-State Response and Forced Response 
10.27
10.5.1 The DC Steady-State 
10.28
10.5.2 The Sinusoidal Steady-State 
10.28
10.5.3 The Periodic Steady-State 
10.29
10.6 Linearity and Superposition Principle in Dynamic Circuits 
10.31
10.7 Unit Impulse Response of Series RL Circuit 
10.34
10.7.1 Zero-State Response for Other Inputs from Impulse Response 
10.37
10.8 Series RL Circuit with Exponential Inputs 
10.43
10.8.1 Zero-State Response for Real Exponential Input 
10.44
10.8.2 Zero-State Response for Sinusoidal Input 
10.45
10.9 General Analysis Procedure for Single Time Constant RL Circuits 
10.48
10.10 Summary 
10.57
10.11 Problems 
10.59