Concept explainers
In the circuit of Fig. 7.117, find ix for t > 0. Let R1 = R2 = 1 kΩ, R3 = 2 kΩ, and C = 0.25 mF.
Figure 7.117
Calculate the current
Answer to Problem 50P
The current
Explanation of Solution
Given data:
Refer to Figure 7.117 in the textbook.
The source current
The value of resistances are
The value of capacitance
Formula used:
Write the general expression to find the complete voltage response for an RC circuit.
Here,
Write the expression to find the time constant for an RC circuit.
Here,
C is the capacitance of the capacitor.
Calculation:
The given Figure 7.117 is redrawn as shown in Figure 1.
For
The switch is kept open at this condition. Therefore, the initial capacitor voltage
For
In Figure 1, the current source
That is,
Figure 2 shows the modified circuit diagram when
In Figure 2, the final capacitor voltage
Figure 2 shows the Thevenin resistance
In Figure 3, the Thevenin resistance is calculated as follows.
Substitute
Substitute the units
Substitute
Figure 4 shows the modified circuit diagram to find the current
In Figure 4, apply Kirchhoff’s current law at node 1.
In Figure 4, apply Kirchhoff’s current law at node
Substitute
Reduce the equation as follows,
Substitute
Reduce the equation as follows,
Conclusion:
Thus, the current
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Chapter 7 Solutions
Fundamentals of Electric Circuits
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