Concept explainers
(a)
Calculate the energy stored in each energy storage element.
(a)
Answer to Problem 70E
The value of energy stored in the inductor
Explanation of Solution
Given data:
Refer to Figure 7.84 in the textbook.
Calculation:
The given circuit is redrawn as shown in Figure 1.
For a DC circuit, at steady state condition, the capacitor acts like open circuit and the inductor acts like short circuit.
Now, the Figure 1 is reduced as shown in Figure 2.
Apply Kirchhoff’s voltage law for loop 1 in Figure 2.
Refer to Figure 2, the current
Substitute
Simplify the above equation to find
Apply Kirchhoff’s voltage law for loop 3 in Figure 2.
Refer to Figure 2, the voltage across the resistor
The voltage
Substitute equation (4) in (3).
Substitute
Substitute equation (2) in (5).
Simplify the above equation to find
Substitute
Refer to Figure 2, the current
Substitute
Refer to Figure 2, the resistor
Write a general expression to calculate the energy stored in a inductor.
Here,
Write a general expression to calculate the energy stored in a capacitor.
Here,
Substitute
Simplify the above equation to find
Substitute
Simplify the above equation to find
Conclusion:
Thus, the value of energy stored in the inductor
(b)
Verify the calculated answers with an appropriate simulation.
(b)
Explanation of Solution
Create the new schematic in LTspice and draw the Figure 1 as shown in Figure 3. Use the Label net option and write VR2 to find voltage across resistor
Choose the Dc op point in Edit simulation Cmd as shown in Figure 4.
After adding the above mentioned commands the circuit becomes as shown in Figure 5.
Now run the simulation, the table will be displayed with the values of current through resistors, capacitor and voltage across the capacitor as shown in Figure 6.
Refer to Figure 6, the value of voltage across the capacitor
Conclusion:
Thus, the calculated answers are verified with an appropriate SPICE simulation.
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Chapter 7 Solutions
Loose Leaf for Engineering Circuit Analysis Format: Loose-leaf
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