26. Capacitors & Dielectrics

What is the equivalent capacitance of the following capacitors?

For the system of capacitors shown in Fig. E$24.16$, find the equivalent capacitance between $b$ and $c$.

You need a capacitance of 50 μF, but you don't happen to have a 50 μF capacitor. You do have a 75 μF capacitor. What additional capacitor do you need to produce a total capacitance of 50 μF? Should you join the two capacitors in parallel or in series?

Find expressions for the equivalent capacitance of (a) N identical capacitors C in parallel and (b) N identical capacitors C in series.

Each capacitor in FIGURE CP26.83 has capacitance C. What is the equivalent capacitance between points a and b?

A 6 μF capacitor, a 10 μF capacitor, and a 16 μF capacitor are connected in series. What is their equivalent capacitance?

What is the equivalent capacitance of the three capacitors in FIGURE EX26.27?

A 2.70-μF capacitor is charged to 435 V and a 4.00-μF capacitor is charged to 525 V. 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?

A 2.70-μF capacitor is charged to 435 V and a 4.00-μF capacitor is charged to 525 V. What is the voltage and charge for each capacitor if plates of opposite sign are connected? [Hint: Charge is conserved.]

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.

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.