Concept explainers
A charge Q is placed on a capacitor of capacitance C. The capacitor is connected into the circuit shown in Figure P26.37, with an open switch, a resistor, and an initially uncharged capacitor of capacitance 3C. The switch is then closed, and the circuit comes to equilibrium. In terms of Q and C, find (a) the final potential difference between the plates of each capacitor, (b) the charge on each capacitor, and (c) the final energy stored in each capacitor. (d) Find the internal energy appearing in the resistor.
Figure P26.37
(a)
Answer to Problem 27.63AP
Explanation of Solution
Given information: The value of capacitor into the circuit is
Explanation:
Formula to calculate the equivalent capacitance of the system when they are connected in parallel.
Here,
Substitute
Thus, the equivalent capacitance of the system when they are connected in parallel is
Formula to calculate the final potential difference between the plates of each capacitor.
Here,
Substitute
Thus, the final potential difference between the plates of each capacitor is
Conclusion:
Therefore, the final potential difference between the plates of each capacitor is
(b)
Answer to Problem 27.63AP
Explanation of Solution
Given information: The value of capacitor into the circuit is
Explanation:
Formula to calculate the charge placed on a capacitor
Here,
Substitute
Thus, the charge placed on a capacitor
Formula to calculate the charge placed on a capacitor
Here,
Substitute
Thus, the charge placed on a capacitor
Conclusion:
Therefore, the charge on capacitor
(c)
Answer to Problem 27.63AP
Explanation of Solution
Given information: The value of capacitor into the circuit is
Explanation:
Formula to calculate the energy stored in the capacitor
Here,
Substitute
Thus, the energy stored in the capacitor
Formula to calculate the energy stored in the capacitor
Here,
Substitute
Thus, the energy stored in the capacitor
Conclusion:
Therefore, the energy stored in the capacitor
(d)
Answer to Problem 27.63AP
Explanation of Solution
Given information: The value of capacitor into the circuit is
Explanation:
Write the expression for the original energy in the resistor.
Here,
Formula to calculate the internal energy appearing in the resistor.
Here,
Substitute
Thus, the internal energy appearing in the resistor is
Conclusion:
Therefore, the internal energy appearing in the resistor is
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Chapter 27 Solutions
Physics For Scientists And Engineers, Volume 2
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