Calculate the current response
Answer to Problem 57P
The current response
Explanation of Solution
Given data:
Refer to Figure 7.123 in the textbook.
The value of inductance
The value of inductance
Formula used:
Write the general expression to find the current response for the RL circuit.
Here,
Write the expression to calculate the time constant for the RL circuit.
Here,
L is the inductance of the inductor.
Write the general expression for the unit step function.
Calculation:
For
The given Figure 7.123 is redrawn as shown in Figure 1. At this condition, the inductor reaches steady state and acts like a short circuit to DC.
In Figure 1, apply Kirchhoff’s current law at node
Simplify the equation as follows,
Now find the initial inductor current
Substitute
Now find the initial inductor current
Substitute
For
Figure 2 shows the modified circuit diagram when the switch is kept in closed position.
Consider the value of resistances
In Figure 2, the switch is closed so that the energies in the inductance
The current response
The time constant in equation (6) can be rewritten as like in equation (2) as follows.
Substitute
Substitute the units
Substitute
Apply the unit step function in equation (3) to equation (9).
The current response
The time constant in equation (10) can be rewritten as like in equation (2) as follows.
Substitute
Substitute the units
Substitute
Apply the unit step function in equation (3) to equation (13).
Convert the unit A to mA.
Conclusion:
Thus, the current response
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Chapter 7 Solutions
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