Concept explainers
Calculate the voltage labeled vx in Fig. 7.52, assuming the circuit has been running a very long time, if (a) a 10 Ω resistor is connected between terminals x and y; (b) a 1 H inductor is connected between terminals x and y; (c) a 1 F capacitor is connected between terminals x and y; (d) a 4 H inductor in parallel with a 1 Ω resistor is connected between terminals x and y.
FIGURE 7.52
(a)
Find the voltage
Answer to Problem 29E
The voltage
Explanation of Solution
Given data:
Value of resistance connected between terminals
Calculation:
The redrawn circuit is shown in Figure 1 as follows:
Here,
The redrawn circuit is shown in Figure 2.
Refer to the Figure 2:
When steady state is reached, all the inductors connected are short circuited and all the capacitors connected are open circuited.
The equivalent resistance for series combination across branch is as follows:
Substitute
The redrawn circuit is shown in Figure 3 as follows:
Refer to the redrawn Figure 3:
The expression for the nodal analysis at node voltage
Here,
The expression for the current across the resistance
The expression for the voltage across the resistance
The current across the resistances
Substitute
Solve for
Substitute
Substitute
Conclusion:
Thus, the voltage
(b)
Find the voltage
Answer to Problem 29E
The voltage
Explanation of Solution
Given Data:
Value of inductor connected between terminals
Calculation:
The redrawn circuit with inductor connected across branch
The redrawn circuit is shown in Figure 4 as follows:
Refer to the Figure 5:
When steady state is reached, the inductor connected across branch
The redrawn circuit is shown in Figure 6 as follows:
The expression for the nodal analysis at node voltage
The expression for the current across the resistance
The expression for the current across the resistance
The current across the resistances
Substitute
Solve for
Substitute
Substitute
Conclusion:
Thus, the voltage
(c)
Find the voltage
Answer to Problem 29E
The voltage
Explanation of Solution
Given data:
Value of capacitor connected between terminals
Calculation:
The redrawn circuit of capacitor connected across branch
Refer to the redrawn Figure 7:
The redrawn circuit is shown in Figure 8 as follows:
When steady state is reached, thecapacitors connected across branch
The redrawn circuit is shown in Figure 9 as follows:
Refer to the Figure 9:
The expression for the nodal analysis at node voltage
The expression for the current across the resistance
The expression for the voltage across the resistance
The current across the resistances
Substitute
Solve for
Substitute
Substitute
Conclusion:
Thus, the voltage
(d)
Find the voltage
Answer to Problem 29E
The voltage
Explanation of Solution
Given Data:
Value of inductor connected between terminal
Value of resistor connected in parallel with inductor across terminal
Calculation:
The redrawn circuit is shown in Figure 10:
Refer to the redrawn Figure 10:
The redrawn circuit is shown in Figure 11 as follows:
When steady state is reached, the inductor connected across branch
The redrawn circuit is shown in Figure 12,
Refer to the Figure 12:
The expression for the nodal analysis at node voltage
The expression for the current across the resistance
The expression for the voltage across the resistance
The current across the resistances
Substitute
Solve for
Substitute
Substitute
Conclusion:
Thus, the voltage
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