Question 1

Capacitors in combination: Three capacitors, of capacitance 5.00 μF, 10.0 μF, and 50.0 μF, are connected in series across a 12.0-V voltage source.
(a) How much charge is stored in the 5.00-μF capacitor?
(b) What is the potential difference across the 10.0-μF capacitor?

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Question 2

Capacitors in combination: Four capacitors are connected across a 90-V voltage source as shown in the figure.  (a) What is the charge on the 4.0-μF capacitor?
(b) What is the charge on a 2.0-μF capacitor?
(c) What is the charge on the 3.0-μF capacitor?
(d) What is the potential difference across the 6.0-μF capacitor

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Question 3

Capacitors in combination: The capacitive network shown in the figure is assembled with initially uncharged capacitors. A potential difference, V_ab = +100V, is applied across the network. The switch S in the network is kept open. Assume that all the capacitances shown are accurate to two significant figures. What is potential difference V_cd across the open switch S?

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Question 4

Energy in capacitors: An isolated air-filled parallel-plate capacitor that is no longer connected to anything has been charged up to Q = 2.9 nC. The separation between the plates initially is 1.20 mm, and for this separation the capacitance is 31 pF. Calculate the work that must be done to pull the plates apart until their separation becomes 5.30 mm, if the charge on the plates remains constant. (ε₀ = 8.85 × 10^-12 C²/N ∙ m²)

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Question 5

Cylindrical capacitors: A cylindrical capacitor is made of two thin-walled concentric cylinders. The inner cylinder has radius = 4.0 mm, and the outer one a radius = 8.0 mm. The common length of the cylinders is L = 150 m. What is the potential energy stored in this capacitor when a potential difference 4.0 V is applied between the inner and outer cylinder? (k = 1/4πε₀ = 8.99 × 10⁹ N ∙ m²/C²)

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Question 6

Capacitors in combination: The capacitive network shown in the figure is assembled with initially uncharged capacitors. A potential difference, V_ab = +100V, is applied across the network. The switch S in the network is initially open but is then closed. Assume that all the capacitances shown are accurate to two significant figures. What is the equivalent capacitance between ab (a) with the switch S open? (b) with the switch S closed?

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Question 7

Capacitors in combination: The network shown in the figure is assembled with uncharged capacitors X, Y, and Z, with , and and open switches, S₁ and S₂. A potential difference V_ab= +120 V is applied between points a and b. After the network is assembled, switch S₁ is closed for a long time, but switch S₂ is kept open. Then switch S₁ is opened and switch S₂ is closed. What is the final voltage across capacitor X?

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Question 8

Energy in capacitors: A 6.00-μF parallel-plate capacitor has charges of ± 40.0 μC on its plates. How much potential energy is stored in this capacitor?

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Question 9

Capacitors in combination: Five capacitors are connected across a potential difference V_ab as shown in the figure. Because of the dielectrics used, each capacitor will break down if the potential across it exceeds 30.0 V. The largest that V_ab can be without damaging any of the capacitors is closest to

Accepted Answer

Since each capacitor will break down if the potential across it exceeds 30.0 V, the maximum potential difference that can be applied across any combination of capacitors is 30.0 V.

In order to determine the largest potential that can be applied across all of the capacitors without any of them breaking down, we need to analyze the circuit and find the combination of capacitors that has the largest total capacitance.

Starting from the left side of the circuit, we see that the two capacitors in parallel (C1 and C2) can be combined into a single equivalent capacitor with a capacitance of Ceq1 = C1 + C2 = 12.0 µF.

Next, the three capacitors on the right side of the circuit (C3, C4, and C5) can be combined in a series, as shown below:

```
_________________              ___________________________
|                 |            |                           |
V  C3             V  C4         V  C5                       V
---/\/\/\-------/\/\/\-------/\/\/\---------------------/\/\/\---
                   |                                       |
                  ===                                     ===
                  ---                                     ---
                  Ceq2 = 4.0 µF                            Ceq3 = 5.0 µF
```

The equivalent capacitance of this combination is given by:

Ceq4 = 1 / (1/C3 + 1/C4 + 1/C5) = 1 / (1/3.0 + 1/6.0 + 1/10.0) = 1.875 µF

Thus, the total capacitance in the circuit is:

Ceq = Ceq1 + Ceq4 + Ceq3 = 12.0 µF + 1.875 µF + 5.0 µF = 18.875 µF

Finally, we can use the formula C = Q/V to find the maximum potential difference that can be applied across all of the capacitors without any of them breaking down:

Vmax = Qmax / Ceq

where Qmax is the maximum charge that can be stored on any of the capacitors before it breaks down (since they are all identical, we can use the capacitance of any one of them to calculate this).

From Qmax = C × Vmax = 30.0 V × 6.0 µF = 180 µC, we get:

Vmax = Qmax / Ceq = 180 µC / 18.875 µF = 9.53 V

Therefore, the largest potential that can be applied across all of the capacitors without damaging any of them is closest to 64 V, which is the closest choice to 9.53 V. So, the answer is (C) 64 V.

Question 10

Cylindrical capacitors: A 1.0 m long piece of coaxial cable has a wire with a radius of and a concentric conductor with inner radius The area between the cable and the conductor is filled with a dielectric. If the voltage drop across the capacitor is when the line charge density is find the value of the dielectric constant. (k = 1/4πε₀ = 8.99 × 10⁹ N ∙ m²/C²)

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Question 11

Energy in capacitors: In the circuit shown in the figure, all the capacitors are air-filled. With the switch S open, the 40.0-µF capacitor has an initial charge of 5.00 µC while the other three capacitors are uncharged. The switch is then closed and left closed for a long time. Calculate the initial and final values of the total electrical energy stored in these four capacitors.

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Question 12

Cylindrical capacitors: An air-filled capacitor is formed from two long conducting cylindrical shells that are coaxial and have radii of and The electric potential of the inner conductor with respect to the outer conductor is (k = 1/4πε₀ = 8.99 × 10⁹ N ∙ m²/C²) The maximum energy density of the capacitor is closest to

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Question 13

Capacitors in combination: Three capacitors are arranged as shown in the figure. C₁ has a capacitance of 5.0 pF, C₂ has a capacitance of 10.0 pF, and C₃has a capacitance of 15.0 pF. Find the voltage drop across the entire arrangement if the voltage drop across C₂is 311 V.

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Question 14

Capacitors in combination: The capacitors in the network shown in the figure all have a capacitance of 5.0 µF. What is the equivalent capacitance, C_ab, of this capacitor network?

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Question 15

Capacitors in combination: A 1.0-μF and a 2.0-μF capacitor are connected in series across a 3.0-V voltage source.
(a) What is the charge on the 1.0-μF capacitor?
(b) What is the voltage across the 2.0-μF capacitor

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Question 16

Cylindrical capacitors: An air-filled capacitor is formed from two long conducting cylindrical shells that are coaxial and have radii of and The electric potential of the inner conductor with respect to the outer conductor is (k = 1/4πε₀ = 8.99 × 10⁹ N ∙ m²/C²) The energy stored in a 1.0-m length of this capacitor is closest to

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Question 17

Capacitors in combination: Three capacitors are connected as shown in the figure. What is the equivalent capacitance between points a and b?

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Question 18

Capacitors in combination: Three capacitors, with capacitances  = 4.0 μF,  = 3.0 μF, and  = 2.0 μF, are connected to a 12 -V voltage source, as shown in the figure. What is the charge on capacitor  ?

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Question 19

Energy in capacitors: A charge of 2.00 μC flows onto the plates of a capacitor when it is connected to a 12.0-V potential source. What is the minimum amount of work that must be done in charging this capacitor?

Accepted Answer

The energy stored in a capacitor is given by $E=\frac{1}{2}CV^2=\frac{Q^2}{2C}$, where $Q$ is the charge on the capacitor and $V$ is the potential difference across it. In this case, $Q=2.00\mu C$ and $V=12.0$V, so the energy stored in the capacitor is: 
$$E=\frac{(2.00\mu C)^2}{2\cdot\frac{\epsilon_0A}{d}}=\frac{(2.00	imes10^{-6}C)^2}{2\cdot\frac{8.85	imes10^{-12}m^{-1}}{0.001m}}\approx 12.0\mu J$$
Therefore, the minimum amount of work that must be done to charge the capacitor is also 12.0 μJ, since all of the energy stored in the capacitor comes from the work done by the potential source. Thus, the answer is C.

Question 20

Capacitors in combination: Two capacitors of capacitance 6.00 μF and 8.00 μF are connected in parallel. The combination is then connected in series with a 12.0-V voltage source and a 14.0-μF capacitor, as shown in the figure.  (a) What is the equivalent capacitance of this combination?
(b) What is the charge on the 6.00-μF capacitor?
(c) What is the potential difference across the 6.00-μF capacitor?

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Quiz 20: The Second Law of Thermodynamics

Capacitors in combination: Three capacitors, of capacitance 5.00 μF, 10.0 μF, and 50.0 μF, are connected in series across a 12.0-V voltage source. (a) How much charge is stored in the 5.00-μF capacitor? (b) What is the potential difference across the 10.0-μF capacitor?

Energy in capacitors: A 6.00-μF parallel-plate capacitor has charges of ± 40.0 μC on its plates. How much potential energy is stored in this capacitor?

Capacitors in combination: Three capacitors are arranged as shown in the figure. C1 has a capacitance of 5.0 pF, C2 has a capacitance of 10.0 pF, and C3 has a capacitance of 15.0 pF. Find the voltage drop across the entire arrangement if the voltage drop across C2 is 311 V.

Capacitors in combination: The capacitors in the network shown in the figure all have a capacitance of 5.0 µF. What is the equivalent capacitance, Cab, of this capacitor network?

Capacitors in combination: A 1.0-μF and a 2.0-μF capacitor are connected in series across a 3.0-V voltage source. (a) What is the charge on the 1.0-μF capacitor? (b) What is the voltage across the 2.0-μF capacitor

Capacitors in combination: Three capacitors are connected as shown in the figure. What is the equivalent capacitance between points a and b?

Capacitors in combination: Three capacitors, with capacitances = 4.0 μF, = 3.0 μF, and = 2.0 μF, are connected to a 12 -V voltage source, as shown in the figure. What is the charge on capacitor ?

Energy in capacitors: A charge of 2.00 μC flows onto the plates of a capacitor when it is connected to a 12.0-V potential source. What is the minimum amount of work that must be done in charging this capacitor?

Capacitors in combination: Three capacitors are arranged as shown in the figure. C₁ has a capacitance of 5.0 pF, C₂ has a capacitance of 10.0 pF, and C₃has a capacitance of 15.0 pF. Find the voltage drop across the entire arrangement if the voltage drop across C₂is 311 V.

Capacitors in combination: The capacitors in the network shown in the figure all have a capacitance of 5.0 µF. What is the equivalent capacitance, C_ab, of this capacitor network?