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(a)
Find the expression of the voltage across an inductor
(a)
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Answer to Problem 1P
The expression of the voltage across an inductor
Explanation of Solution
Given data:
The current through an inductor is
The inductor value is,
Formula used:
Write the general expression to find the voltage across an inductor as,
Here,
L is the value of inductance of the inductor,
Calculation:
Substitute
Conclusion:
Thus, the expression of the voltage across an inductor
(b)
Calculate the power at the inductor terminals at time of
(b)
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Answer to Problem 1P
The power at the inductor terminals at time of
Explanation of Solution
Calculation:
Given that
At time
At time
At time
At time
At time
Calculate the voltage at
Write the formula to find the power in an inductor at
Substitute
PSpice simulation:
Use all the above calculated values to give as an input to the PSpice simulation.
From the given information, the current passing through an inductor and here a small resistor is connected in series with inductor to avoid the simulation error.
Draw the circuit as shown in below Figure 1.
Provide the simulation settings as shown in below Figure 2.
Now, save and run the simulation, then the plot for the input current and voltage across an inductor will be displays as shown in Figure 3.
From the Figure 3, the first function is used to read the voltage at
The power calculated at
Conclusion:
Thus, the power at the inductor terminals at time of
(c)
Check whether an inductor is delivering the power or absorbing the power.
(c)
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Answer to Problem 1P
An inductor is delivering the power.
Explanation of Solution
Discussion:
The power calculated in an inductor has the negative sign which indicates that the power is delivering by an inductor.
Conclusion:
Thus, an inductor is delivering the power.
(d)
Calculate the energy stored in an inductor in micro joules at
(d)
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Answer to Problem 1P
The energy stored in an inductor in at
Explanation of Solution
Discussion:
From the simulation results shown in Part (b), the fourth equation is written to calculate energy stored in an inductor. From the Figure 3, the energy stored in an inductor in at
Conclusion:
Thus, the energy stored in an inductor in at
(e)
Find the maximum energy, and also find the instant of time that occurs.
(e)
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Answer to Problem 1P
The maximum energy is
Explanation of Solution
Discussion:
When the current is maximum energy in an inductor also maximum, since the square of current is directly proportional to the energy stored.
From the Figure 3, it is calculated that maximum current as 662.2 mA, that occurs at
Conclusion:
Thus, the maximum energy is
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Chapter 6 Solutions
Electric Circuits. (11th Edition)
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