Concept explainers
Obtain the inductor current for both t < 0 and t > 0 in each of the circuits in Fig. 7.120.
(a)
Calculate the value of inductor current
Answer to Problem 54P
The value of inductor current
Explanation of Solution
Given data:
Refer to Figure 7.120 in the textbook.
The value of inductance L in Figure 7.120(a) is
Formula used:
Write the general expression to find the complete response of current 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.
Calculation:
Figure 1 shows the modified circuit diagram when
In Figure 1, the switch is kept in open position for all
Therefore, the inductor current
Figure 2 shows the modified circuit diagram when the switch is kept in close position for all
Apply Kirchhoff’s current law at node a.
Rearrange the equation as follows,
The final inductor current
Substitute
Figure 3 shows the equivalent resistance at the inductor terminal.
In Figure 3, the equivalent resistance is calculated as follows.
Substitute
Substitute the units
Substitute
Therefore, the inductor current
Conclusion:
Thus, the value of inductor current
(b)
Calculate the value of inductor current
Answer to Problem 54P
The value of inductor current
Explanation of Solution
Given data:
Refer to Figure 7.120 in the textbook.
The value of inductance L in Figure 7.120(b) is
Calculation:
Figure 4 shows the modified circuit diagram when switch is kept open for a long time at
In Figure 4,
Rearrange the equation as follows,
Therefore, the inductor current
Figure 5 shows the redrawn circuit when switch is kept in closed position at
In Figure 5, apply Kirchhoff’s current law at node v.
Rearrange the equation as follows,
The final inductor current
Substitute
Figure 6 shows the equivalent resistance at the inductor terminal.
In Figure 6, the equivalent resistance is calculated as follows.
Substitute
Substitute the units
Substitute
Therefore, the inductor current
Conclusion:
Thus, the value of inductor current
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Chapter 7 Solutions
Fundamentals of Electric Circuits
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