The circuit in Figure P27.85 shows four capacitors connected to a battery. The switch S is initially open, and all capacitors have reached their final charge. The capacitances are C1 = 6.00 μF, C2 = 12.00 μF, C3 = 8.00 μF, and C4 = 4.00 μF. a. Find the potential difference across each capacitor and the charge stored in each. b. The switch is now closed. What is the new final potential difference across each capacitor and the new charge stored in each?
Figure P27.85
(a)
The potential difference across the capacitors and the charge stores in each capacitor.
Answer to Problem 85PQ
The charge stored in
The potential difference across the capacitors
Explanation of Solution
The circuit diagram,
Since, the capacitors
Write the expression to find the equivalent capacitance on
Here,
Substitute
Write the expression to find the charges on
Here,
Substitute
Write the expression to find the equivalent capacitance on
Here,
Substitute
Write the expression to find the charges on
Here,
Substitute
Write the equation to find the voltage across the capacitor.
Conclusion:
Substitute
Substitute
Substitute
Substitute
Therefore, the charge stored in
The potential difference across the capacitors
(b)
The potential difference across the capacitors and the charge stores in each capacitor when the switch is closed.
Answer to Problem 85PQ
The charge stored in
The potential difference across the capacitors
Explanation of Solution
The circuit diagram,
When the switch is closed, the capacitors
Write the expression to find the equivalent capacitance on
Here,
Substitute
Write the expression to find the equivalent capacitance on
Here,
Substitute
Write the expression to find the equivalent capacitance of the circuit.
Here,
Substitute
Write the expression to find the charges on the capacitors.
Here,
Substitute
Write the equation to find the voltage across the capacitor.
Conclusion:
Substitute
Substitute
Therefore, the charge stored in
The potential difference across the capacitors
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Chapter 27 Solutions
Physics for Scientists and Engineers: Foundations and Connections
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