26. Capacitors & Dielectrics

What is charge and voltage across each capacitor below?

What is the voltage of the battery below?

What is the charge on the 5 F capacitor? (hint:be careful with series vs parallel)

What are the charge on and the potential difference across each capacitor in FIGURE P26.57?

Six identical capacitors with capacitance C are connected as shown in FIGURE P26.59. What is the potential difference between points a and b?

Initially, the switch in FIGURE P26.61 is in position A and capacitors C₂ and C₃ are uncharged. Then the switch is flipped to position B. Afterward, the voltage across C₁ is 4.0 V. What is the emf of the battery?

Capacitors C₁ = 10 μF and C₂ = 20 μF are each charged to 10 V, then disconnected from the battery without changing the charge on the capacitor plates. The two capacitors are then connected in parallel, with the positive plate of C₁ connected to the negative plate of C₂ and vice versa. Afterward, what are the charge on and the potential difference across each capacitor?

The label rubbed off one of the capacitors you are using to build a circuit. To find out its capacitance, you place it in series with a 10 μF capacitor and connect them to a 9.0 V battery. Using your voltmeter, you measure 6.0 V across the unknown capacitor. What is the unknown capacitor's capacitance?

You have two identical capacitors and an external potential source.

(a) Compare the total energy stored in the capacitors when they are connected to the applied potential in series and in parallel.

(b) Compare the maximum amount of charge stored in each case.

(c) Energy storage in a capacitor can be limited by the maximum electric field between the plates. What is the ratio of the electric field for the series and parallel combinations?

In Fig. E$24.20$, $C_1=6.00$ $\mu$F, $C_2=3.00$ $\mu$F, and $C_3=5.00$ $\mu$F. The capacitor network is connected to an applied potential $V_{ab}$.

(a) After the charges on the capacitors have reached their final values, the charge on $C_2$ is $30.0$ mC. What are the charges on capacitors $C_1$ and $C_3$?

(b) What is the applied voltage $V_{ab}$?

Figure E$24.14$ shows a system of four capacitors, where the potential difference across ab is $50.0$ V. How much charge is stored in each of the $10.0$-$\mu$F and the $9.0$-$\mu$F capacitors?

Figure E$24.14$ shows a system of four capacitors, where the potential difference across ab is $50.0$ V. How much charge is stored by this combination of capacitors?

(I) The variable capacitor in the tuner of an AM radio has a capacitance of 1800 pF when the radio is tuned to a station at 550 kHz. What must the capacitance be for a station near the other end of the dial, 1610 kHz?

(II) In the capacitance bridge shown in Fig. 24–28, a voltage V₀ is applied and the variable capacitor C₁ is adjusted until there is zero voltage between points a and b as measured on the voltmeter (). Determine the unknown capacitance C_x if C₁ = 8.9 μF and the fixed capacitors have C₂ = 16.0 μF and C₃ = 4.8 μF No charge flows through the voltmeter when it reads zero.)