Concept explainers
(a)
The equivalent capacitance of the system.
(a)
Answer to Problem 19P
The equivalent capacitance of the system is
Explanation of Solution
Write the expression for equivalent capacitance for upper capacitor connected in series.
Here,
Write the expression for equivalent capacitance for lower capacitor
Here,
Write the expression for equivalent capacitance for capacitor
Here,
Conclusion:
Substitute
Substitute
Substitute
Therefore, the equivalent capacitance for the system is
(b)
The charge on each capacitor.
(b)
Answer to Problem 19P
The charge in capacitor
Explanation of Solution
For series connection the charge remains constant.
Write the expression for the charge in the upper row.
Here,
Write the expression for the charge in the lower row.
Here,
Conclusion:
Substitute
The charge on
Substitute
The charge on
Therefore, the charge in capacitor
(c)
The potential difference across each capacitor.
(c)
Answer to Problem 19P
The potential difference in capacitor
Explanation of Solution
Write the expression to calculate the potential difference across
Here,
Write the expression to calculate the potential difference across
Here,
Write the expression to calculate the potential difference across
Here,
Write the expression to calculate the potential difference across
Here,
Conclusion:
Substitute
Substitute
Substitute
Substitute
Therefore, the potential difference in capacitor
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Chapter 26 Solutions
Physics: for Science.. With Modern. -Update (Looseleaf)
- 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_forwardFor the system of capacitors shown in Figure P16.41, find (a) the equivalent capacitance of the system, (b) the charge on each capacitor, and (c) the potential difference across each capacitor. Figure P16.41 Problems 41 and 60.arrow_forward
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- Find the equivalent capacitance between points a and b in the combination of capacitors shown in Figure P20.51. Figure P20.51arrow_forwardA parallel-plate capacitor has square plates of side s = 2.50 cm and plate separation d = 2.50 mm. The capacitor is charged by a battery to a charge Q = 4.00 C, after which the battery is disconnected. A porcelain dielectric ( = 6.5) is then inserted a distance y = 1.00 cm into the capacitor (Fig. P27.88). Hint: Consider the system as two capacitors connected in parallel. a. What is the effective capacitance of this capacitor? b. How much energy is stored in the capacitor? c. What are the magnitude and direction of the force exerted on the dielectric by the plates of the capacitor? Figure P27.88arrow_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
- Four 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_forwardConsider the combination of capacitors in Figure P16.42. (a) Find the equivalent single capacitance of the two capacitors in series and redraw the diagram (called diagram 1) with this equivalent capacitance. (b) In diagram 1, find the equivalent capacitance of the three capacitors in parallel and redraw the diagram as a single battery and single capacitor in a loop. (c) Compute the charge on the single equivalent capacitor. (d) Returning to diagram 1, compute the charge on each individual capacitor. Does the sum agree with the value found in part (c)? (e) What is the charge on the 24.0-F capacitor and on the 8.00-F capacitor? Compute the voltage drop across (f) the 24.0-F capacitor and (g) the 8.00-F capacitor. Figure P16.42arrow_forwardThree capacitors are connected to a battery as shown in Figure P20.50. 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 P20.50arrow_forward
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