Concept explainers
Three capacitors are connected to a battery as shown in Figure P25.10. Their capacitances are C1 = 3C, C2 = C, and C3 = 5C. (a) What is the equivalent capacitance of this set of capacitors? (b) State the ranking of the capacitors according to the charge they store from largest to smallest. (c) Rank the capacitors according to the potential differences across them from largest to smallest. (d) What If? Assume C3 is increased. Explain what happens to the charge stored by each capacitor.
Figure P25.10
(a)
Answer to Problem 26.20P
Explanation of Solution
Given information: The value of capacitor 1 is
Explanation:
The capacitors
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
The capacitors
Formula to calculate the equivalent capacitance of the system when they are connected in series.
Here,
Substitute
Thus, the equivalent capacitance of this set of capacitors is
Conclusion:
Therefore, the equivalent capacitance of this set of capacitors is
(b)
Answer to Problem 26.20P
Explanation of Solution
Given information: The value of capacitor 1 is
Explanation:
Calculate the voltage across
Here,
Substitute
Calculate the charge for the capacitor
Here,
Substitute
Thus, the charge for the capacitor
Calculate the charge for the capacitor
Here,
Substitute
Thus, the charge for the capacitor
Calculate the voltage across
Here,
Substitute
Calculate the charge for the capacitor
Here,
Substitute
Thus, the charge for the capacitor
The ranking of the capacitors according to the charge they store from largest to smallest is
Thus, the ranking of the capacitors according to the charge they store from largest to smallest is
Conclusion:
Therefore, the ranking of the capacitors according to the charge they store from largest to smallest is
(c)
Answer to Problem 26.20P
Explanation of Solution
Given information: The value of capacitor 1 is
Explanation:
Calculate the potential difference across
Here,
Substitute
Thus, the potential difference across
Calculate the potential difference across
Here,
Substitute
Thus, the potential difference across
Calculate the potential difference across
Here,
Substitute
Thus, the potential difference across
The ranking of the capacitors according to the potential differences across them from largest to smallest is
Thus, the ranking of the capacitors according to the potential differences across them from largest to smallest is
Conclusion:
Therefore, the ranking of the capacitors according to the potential differences across them from largest to smallest is
(d)
Answer to Problem 26.20P
Explanation of Solution
Given information: The value of capacitor 1 is
Explanation:
If the value of capacitor 3 is increased, the total capacitance will increase which results in increasing the total charge.
Due to this, the charge across capacitor 1 increases.
Since, the charge across capacitor 1 is directly proportional to the voltage across the capacitor 1. So, the voltage across
Since the voltage across the capacitor 2 decreases, charge across the capacitor 2 also decreases and the voltage across the capacitor 3 decreases, charge across the capacitor 3 also decreases.
Thus, if
Conclusion:
Therefore, if
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Chapter 26 Solutions
EBK PHYSICS FOR SCIENTISTS AND ENGINEER
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