Concept explainers
A source-free RC circuit has R = 4 kΩ and C = 22 μF, and with the knowledge that v(0) = 5 V, (a) write an expression for v(t) valid for t > 0; (b) compute v(t) at t = 0, t = 50 ms, and t = 500 ms; and (c) calculate the energy stored in the capacitor at t = 0, t = 50 ms, and t = 500 ms.
(a)
Write an expression for
Answer to Problem 1E
The expression for
Explanation of Solution
Given Data:
The initial value of the voltage across the capacitor is
The resistance of
The capacitance of
Formula used:
The expression for the time constant for
Here,
The expression for the voltage across the capacitor for
Here,
Calculation:
Substitute
Substitute
Conclusion:
Thus, the expression for
(b)
Find
Answer to Problem 1E
The value of the voltage
Explanation of Solution
Given Data:
The time at which voltage has to be calculated is
Calculation:
Substitute
Substitute
Substitute
Conclusion:
Thus, the value of the voltage
(c)
Find the value of energy stored in the capacitor for different time periods.
Answer to Problem 1E
The energy stored in the capacitor at
Explanation of Solution
Given Data:
The time is
Formula used:
The expression for the energy stored in the capacitor is as follows.
Here,
Calculation:
Substitute
Substitute
Substitute
Conclusion:
Thus, the energy stored in the capacitor at
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