26. Capacitors & Dielectrics

What is the equivalent capacitance of the following capacitors?

(II) A 2.70-μF capacitor is charged to 435 V and a 4.00-μF capacitor is charged to 525 V.

(a) These capacitors are then disconnected from their batteries. Then the positive plates are connected to each other and the negative plates are connected to each other. What will be the potential difference across each capacitor and the charge on each?

(II) A 2.70-μF capacitor is charged to 435 V and a 4.00-μF capacitor is charged to 525 V.

(b) What is the voltage and charge for each capacitor if plates of opposite sign are connected? [Hint: Charge is conserved.]

(II) A 0.50-μF and a 0.80-μF capacitor are connected in series to a 9.0-V battery. Calculate

(a) the potential difference across each capacitor and

(b) the charge on each.

(c) Repeat parts (a) and (b) assuming the two capacitors are in parallel.

(II) Two capacitors connected in parallel produce an equivalent capacitance of 32.9-μF, but when connected in series the equivalent capacitance is only 5.5 μF. What is the individual capacitance of each capacitor?

(II) When two uncharged capacitors are connected in parallel and then connected to a battery, the total stored energy is 6.0 times greater than when they are connected in series and then connected to the same battery. What is the ratio of the two capacitances?

A multilayer “film” capacitor has a maximum voltage rating of 100 V and a capacitance of 1.0 μF. It is made from alternating sheets of very thin metal foil connected together, separated by films of polyester dielectric. The sheets are 12.0 mm by 14.0 mm and the total thickness of the capacitor is 6.0 mm (not counting the thickness of the insulator on the outside). The metal foils are actually very thin layers of metal deposited directly on the dielectric, so most of the thickness of the capacitor is due to the dielectric. The dielectric strength of the polyester is about 30 x 10⁶ V/m. Estimate the dielectric constant of the polyester material in the capacitor.

(II) Three conducting plates, each of area A, are connected as shown in Fig. 24–23.

(a) Are the two capacitors thus formed connected in series or in parallel?

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(II) A 7.7-μF capacitor is charged by a 185-V battery (Fig. 24–21a) and then is disconnected from the battery. When this capacitor (C₁) is then connected (Fig. 24–21b) to a second (initially uncharged) capacitor, C₂ , the final voltage on each capacitor is 15 V. What is the value of C₂ ? [Hint: Charge is conserved.]

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(II) Suppose in Fig. 24–27 that C₁ = C₃ = 8.0μF , C₂ = C₄ = 16μF, and Q₃ = 21μC. Determine

(a) the charge on each of the other capacitors,

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(II) Answer the same questions as for Problem 25, for the three plates connected as shown in Fig. 24–24.

(a) Are the two capacitors thus formed connected in series or in parallel?

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