1. ECE 201 Circuit Theory 11 Step Response of an RL Circuit Find the current in the loop or the voltage across the inductor after the switch is closed at t = 0.

2. ECE 201 Circuit Theory 12 Write KVL around the loop Solve for the highest-order derivative Differential change in current

3. ECE 201 Circuit Theory 13 Separate the variables Introduce dummy variables x and y Integrate to ln Invert to exponential Final expression for i(t)

4. ECE 201 Circuit Theory 14 Take a closer look at the current When the initial energy is equal to zero Plot shown on the next slide

5. ECE 201 Circuit Theory 15

6. 6 Look at the derivative at t = 0

7. ECE 201 Circuit Theory 17 If the current continued at this rate Plot shown on next slide

8. ECE 201 Circuit Theory 18

9. 9 What About the Voltage Across the Inductor?

10. ECE 201 Circuit Theory 110

11. ECE 201 Circuit Theory 111 Look at the derivative of the voltage

12. ECE 201 Circuit Theory 112 If the voltage continued at this rate

13. ECE 201 Circuit Theory 113