A series circuit consisting of an uncharged 2.0-µF capacitor and a 10-MΩ resistor is connected across a 100-V power source. What are the current in the circuit and the charge on the capacitor (a) after one time constant, and (b) when the capacitor has acquired 90 percent of its final charge?
(a)
The current in the circuit and charge across the capacitor in the RC circuit after one time constant when a series circuit consisting of uncharged
Answer to Problem 30SP
Solution:
Explanation of Solution
Given data:
Capacitance of the capacitor is
Resistance of the resistor is
The emf of the voltage source is
Formula used:
When a capacitor is connected to a battery, in the beginning the capacitor carries the current that keeps on decreasing till it is fully charged. Once the capacitor is fully charged the current through it is zero. This happens because a capacitor acts as a short circuit when it is uncharged and as an open circuit when it is fully charged.
The expression of current flowing through an RC circuit is
Here,
The expression of the time constant in term of resistance and capacitance is
The maximum current in the circuit at starting is
Here,
The expression for instantaneous charge stored in the capacitor is
Here,
The maximum charge stored in the capacitor.
Explanation:
Recall the expression of current flowing through an RC circuit.
Substitute
Substitute
Recall the expression of instantaneous charge stored in the capacitor in RC circuit.
Substitute
Substitute
Conclusion:
The current in the RC circuit is
(b)
The current in the RC circuit and charge across the capacitor when the capacitor acquires 90 percent of its final chargewhen a series circuit consisting of uncharged
Answer to Problem 30SP
Solution:
Explanation of Solution
Given data:
Capacitance of the capacitor is
Resistance of the resistor is
The emf of the voltage source is
Formula used:
When a capacitor is connected to a battery, in the beginning the capacitor carries the current that keeps on decreasing till it is fully charged. Once the capacitor is fully charged the current through it is zero. This happens because a capacitor acts as a short circuit when it is uncharged and as an open circuit when it is fully charged.
The expression for instantaneous charge stored in the capacitor is
Here,
The maximum charge stored in the capacitor is
Here,
The expression of current flowing through an RC circuit when capacitor is charging is
Here,
The expression of the time constant in term of resistance and capacitance is
The maximum current in the circuit at starting is
Explanation:
Recall the expression for instantaneous charge stored in the capacitor.
The capacitor stored
Substitute
Take logarithm on both sides
Substitute
Recall the expression of current flowing through an RC circuit when capacitor is charging.
Substitute
Substitute
Substitute
Recall the expression of the maximum charge stored in the capacitor.
Substitute
The capacitor acquired 90 percent of its final charge
Substitute
Conclusion:
The current in the RC circuit is
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Chapter 34 Solutions
Schaum's Outline of College Physics, Twelfth Edition (Schaum's Outlines)
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