
Concept explainers
In the circuit in Fig. 6.64, let is = 4.5e−2t mA and the voltage across each capacitor is equal to zero at t = 0. Determine v1 and v2 and the energy stored in each capacitor for all t > 0.
Figure 6.64
For Prob. 6.32.

Find the expression for the voltage
Answer to Problem 32P
The expression for the voltage
Explanation of Solution
Given data:
Refer to Figure 6.64 in the textbook.
The value of the current in the circuit
The voltage across the capacitor at
Calculation:
The given circuit is redrawn as Figure 1.
Refer to Figure 1, the capacitors
Write the expression to calculate the equivalent capacitance for the parallel connected capacitors.
Here,
Substitute
The reduced circuit of the Figure 1 is drawn as Figure 2.
Write the expression to calculate the voltage across the equivalent capacitor
Here,
Substitute
Simplify the equation to find
Refer to Figure 2, the capacitors
Substitute
Refer to Figure 1, the capacitors
Write the expression to calculate the energy stored in the capacitor 1.
Here,
Substitute
Simplify the equation to find
Write the expression to calculate the energy stored in the capacitor 2.
Substitute
Simplify the equation to find
Write the expression to calculate the energy stored in the capacitor 3.
Here,
Substitute
Simplify the equation to find
Conclusion:
Thus, the expression for the voltage
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Chapter 6 Solutions
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