ECE 201 Circuit Theory I1 Step Response Circuit’s behavior to the sudden application of a DC voltage or current. Energy is being stored in the inductor or capacitor

ECE 201 Circuit Theory I2 Step Response of an RL Circuit The switch is closed at t = 0. Determine the current i(t) and the voltage v(t) for t>0. Allow for the possibility of an initial current I 0. i(t)+ v(t) -

ECE 201 Circuit Theory I3 Step Response of a RL Circuit Write KVL around the loop. i(t) + v(t) -

ECE 201 Circuit Theory I4

5 Look at the result Consider the case when there is no initial current in the inductor.

ECE 201 Circuit Theory I6 Plot the current i(t)

ECE 201 Circuit Theory I7 Determine the voltage v(t)

ECE 201 Circuit Theory I8 Plot the voltage v(t)

ECE 201 Circuit Theory I9 Example 7.5 The switch has been in position “a” for a long time. At time t = 0, the switch moves from position a to position b. The switch is a “make- before- break” type: that is, the connection at position b is established before the connection at position a is broken, so there is no interruption of the current through the inductor. + v(t) - i(t)

ECE 201 Circuit Theory I10 Determine the initial value of the current The 200mH inductor looks like a short circuit and carries an initial current of 8A upwards. Therefore, I 0 = -8A. I 0 = - 8A

ECE 201 Circuit Theory I11 Determine the final value of the current and the time constant The final value of the current is (24V/2Ω) = 12A The time constant is (L/R) = (200mH/2Ω) = 100ms i(∞)

ECE 201 Circuit Theory I12 i(t)

ECE 201 Circuit Theory I13 Complete Solution for the Current and Voltage The current in an inductor cannot change instantaneously –Let t = (0-) be the time just before the switch is opened, and t = (0+) be the time just after the switch is opened –Then i(0-) = i(0+) =I 0, and

ECE 201 Circuit Theory I14 Determine the initial voltage across the inductor just after the switch moves to “b”

ECE 201 Circuit Theory I15 Does this result make sense? - v R (0 + ) + + v L (0 + ) - i(0 + ) R1 adds to the battery voltage

ECE 201 Circuit Theory I16 Determine the time it takes for the inductor voltage to reach 24 Volts

ECE 201 Circuit Theory I17 Plot i(t) and v(t)

ECE 201 Circuit Theory I18

ECE 201 Circuit Theory I19 Oscilloscope Results