Concept explainers
(a)
Find the energy stored in the element at time
(a)
Answer to Problem 69E
The energy stored in the element at time
Explanation of Solution
Formula used:
Write a general expression to calculate the energy stored in an capacitor.
Here,
Given data:
Refer to Figure 7.83 in the textbook.
The value of initial voltage across the capacitor
Calculation:
Substitute
Substitute
Simplify the above equation to find
Conclusion:
Thus, the energy stored in the element at time
(b)
Explain whether the energy stored in the capacitor remains same for time
(b)
Answer to Problem 69E
No, the energy is not same in the capacitor for time
Explanation of Solution
Refer to Figure 7.83, it shows an
Due to the presence of resistor in a circuit, there is a voltage drop across the resistor which reduces the voltage across the capacitor. Therefore, the resistor slowly dissipate the energy stored in a capacitor for time
Conclusion:
Thus, the energy is not same in the capacitor for time
(c)
Determine the value of
(c)
Answer to Problem 69E
The value of
Explanation of Solution
Calculation:
Create the new schematic in LTspice with series connected resistor and inductor of given circuit as shown in Figure 1.
Using SPICE Directive mention the command .ic V(Cap_voltage)=9 as shown in Figure 2.
Enter the stop time as 2.5s, time to start saving data as 0, and maximum Timestep as 10ms in Edit simulation Cmd as shown in Figure 3. Use label net option and mention Cap_voltage.
After adding the Spice directives the circuit shows as in Figure 4.
Now run the simulation and place the probe at the node of capacitor, the plot of the voltage across the capacitor with respect to time is shown as shown in Figure 5.
By placing the cursor on the graph, we obtain the current values for different time as shown in below.
For time
For time
For time
For time
Conclusion:
Thus, the value of
(d)
Find the fraction of initial energy remains in the capacitor at time
(d)
Answer to Problem 69E
The fraction of initial energy remains in the capacitor at time
Explanation of Solution
Calculation:
Refer to part (b), the value of voltage at time
Substitute
Substitute
Simplify the above equation to find
Substitute
Substitute
Simplify the above equation to find
The fraction of initial energy remains stored in the capacitor at time
Substitute
The fraction of initial energy remains stored in the capacitor at time
Substitute
Conclusion:
Thus, the fraction of initial energy remains in the capacitor at time
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Chapter 7 Solutions
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