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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

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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) -

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

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ECE 201 Circuit Theory I4

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

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

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

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

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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)

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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

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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(∞)

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ECE 201 Circuit Theory I12 i(t)

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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

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

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

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

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

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ECE 201 Circuit Theory I18

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ECE 201 Circuit Theory I19 Oscilloscope Results

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