Concept explainers
(a)
The equivalent capacitance for the network given.
(a)
Answer to Problem 28PQ
The equivalent capacitance of the combination is
Explanation of Solution
Write the formula for equivalent capacitance of capacitors in series.
Here,
Write the formula for equivalent capacitance of capacitors in parallel.
Here,
The capacitor
Write the formula for the resultant of
Here,
The capacitance
Write the formula for the equivalent capacitance of the given combination.
Here,
Solve the above equation to get expression for
Conclusion:
Substitute
The equivalent capacitance of the combination is
(b)
The charge stored in each of the capacitors.
(b)
Answer to Problem 28PQ
The charge on capacitor
Explanation of Solution
The capacitors in series
Write the formula for the charge on equivalent capacitor.
Here,
Write the formula for the voltage across capacitor
Here,
Write the formula for the charge across
Here,
Write the formula for the charge across
Here,
Conclusion:
Substitute
Substitute
Substitute
Substitute
The charge on capacitor
(c)
The voltage across each of the capacitors.
(c)
Answer to Problem 28PQ
The voltage across
Explanation of Solution
The capacitors in series
Write the formula for the charge on equivalent capacitor.
Here,
Write the formula for the voltage across capacitor
Here,
Write the formula for the voltage across
Here,
Conclusion:
Substitute
Substitute
Substitute
The voltage across
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Chapter 27 Solutions
Physics for Scientist and Engineers (Foundations And Connection; Volume I and II) LLF edition
- An arrangement of capacitors is shown in Figure P27.23. a. If C = 9.70 105 F, what is the equivalent capacitance between points a and b? b. A battery with a potential difference of 12.00 V is connected to a capacitor with the equivalent capacitance. What is the energy stored by this capacitor? Figure P27.23 Problems 23 and 24.arrow_forwardFind (a) the equivalent capacitance of the capacitors in Figure P26.26, (b) the charge on each capacitor, and (c) the potential difference across each capacitor.arrow_forwardGiven the arrangement of capacitors in Figure P27.23, find an expression for the equivalent capacitance between points a and b. Figure P27.23 Problems 23 and 24.arrow_forward
- 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 P25.10arrow_forwardConsider an infinitely long network with identical capacitors arranged as shown in Figure P27.82. Determine the equivalent capacitance of such a network. Each capacitor has a capacitance of 1.00 F.arrow_forwardIn Figure P27.7, capacitor 1 (C1 = 20.0 F) initially has a potential difference of 50.0 V and capacitor 2 (C2 = 5.00 F) has none. The switches are then closed simultaneously. a. Find the final charge on each capacitor after a long time has passed. b. Calculate the percentage of the initial stored energy that was lost when the switches were closed. FIGURE P27.7arrow_forward
- Three capacitors having capacitances 8.4, 8.4, and 4.2 F are connected in series across a 36.0-V potential difference, (a) What is the total energy stored in all three capacitors? (b) The capacitors are disconnected from the potential difference without allowing them to discharge. They are then reconnected in parallel with each other with the positively charged plates connected together. What is the total energy now stored in the capacitors?arrow_forwardFour capacitors are connected as shown in Figure P25.11. (a) Find the equivalent capacitance between points a and b. (b) Calculate the charge on each capacitor, taking Vab = 15.0 V. Figure P25.11arrow_forwardA Pairs of parallel wires or coaxial cables are two conductors separated by an insulator, so they have a capacitance. For a given cable, the capacitance is independent of the length if the cable is very long. A typical circuit model of a cable is shown in Figure P27.87. It is called a lumped-parameter model and represents how a unit length of the cable behaves. Find the equivalent capacitance of a. one unit length (Fig. P27.87A), b. two unit lengths (Fig. P27.87B), and c. an infinite number of unit lengths (Fig. P27.87C). Hint: For the infinite number of units, adding one more unit at the beginning does not change the equivalent capacitance.arrow_forward
- Find the charge on each of the capacitors in Figure P16.43. Figure P16.43arrow_forwardA pair of capacitors with capacitances CA = 3.70 F and CB = 6.40 F are connected in a network. What is the equivalent capacitance of the pair of capacitors if they are connected a. in parallel and b. in series?arrow_forward(a) Find the equivalent capacitance between points a and b for the group of capacitors connected as shown in Figure P20.44. Take C1 = 5.00 F, C2 = 10.0 F, and C3 = 2.00 F. (b) What charge is stored on C3 if the potential difference between points a and b is 60.0 V? Figure P20.44arrow_forward
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