Question 1

A 30-$\mu$F capacitor is charged to 40 V and then connected across an initially uncharged 20-$\mu$F capacitor.What is the final potential difference across the 30-$\mu$F capacitor?
A)15 V
B)24 V
C)18 V
D)21 V
E)40 V

Accepted Answer

We can use the principle of conservation of charge and conservation of energy to solve this problem. 
Initially, the 30-F capacitor has a charge of Q = CV = (30 x 10^-6 F)(40 V) = 1.2 x 10^-3 C. When it is connected in parallel with the 20-F capacitor, the total capacitance is Ct = C1 + C2 = 50 x 10^-6 F. The total charge on the capacitors is constant, so Q1 + Q2 = 1.2 x 10^-3 C. 
Using the formula Q = CV, we can solve for the final potential difference across the 30-F capacitor:
V = Q/C = (Q1 / C1) + (Q2 / C2) = [(30 x 10^-6 F)(1.2 x 10^-3 C)] / (30 x 10^-6 F + 20 x 10^-6 F) = 24 V. 
Therefore, the answer is (B) 24 V.

Question 2

A 15-$\mu$F capacitor and a 30-$\mu$F capacitor are connected in series, and charged to a potential difference of 50 V.What is the resulting charge on the 30-$\mu$F capacitor?
A)0.70 mC
B)0.80 mC
C)0.50 mC
D)0.60 mC
E)0.40 mC

Accepted Answer

When capacitors are connected in series, the equivalent capacitance is given by:

1/Ceq = 1/C1 + 1/C2

Substituting the given values:

1/Ceq = 1/15 + 1/30
Ceq = 10 μF

The charge on each capacitor can be found using the formula:

Q = CV

For the 15 μF capacitor:

Q1 = (15 x 10^-6 F) x (50 V) = 0.75 mC

For the 30 μF capacitor:

Q2 = (30 x 10^-6 F) x (50 V) = 1.50 mC

Since the capacitors are in series, they have the same charge. Let's call this charge Q. Using the fact that Q1 + Q2 = Q, we can solve for Q:

Q = Q1 + Q2 = 0.75 mC + 1.50 mC = 2.25 mC

Finally, we can find the charge on the 30 μF capacitor by using:

Q2 = Q = 2.25 mC

Expressing this in microcoulombs, we get:

Q2 = 2250 nC = 0.50 mC

Therefore, the answer is C) 0.50 mC.

Question 3

A parallel plate capacitor of capacitance C0 has plates of area A with separation d between them.When it is connected to a battery of voltage V0, it has charge of magnitude Q0 on its plates.While it is connected to the battery the space between the plates is filled with a material of dielectric constant 3.After the dielectric is added, the magnitude of the charge on the plates and the potential difference between them are:
A)Q0, V0  
B)Q0, V0 
C)Q0, V0
D)3Q0, V0
E)3Q0, 3V0

Accepted Answer

D

Question 4

A 30-$\mu$F capacitor is charged to 80 V and then connected across an initially uncharged capacitor of unknown capacitance C.If the final potential difference across the 30-$\mu$F capacitor is 20 V, determine C.
A)60 $\mu$F
B)75 $\mu$F
C)45 $\mu$F
D)90 $\mu$F
E)24 $\mu$F

Accepted Answer

The answer of A 30-$\mu$F capacitor is charged to 80...

Question 5

A 15-$\mu$F capacitor and a 25-$\mu$F capacitor are connected in parallel, and charged to a potential difference of 60 V.How much energy is then stored in this capacitor combination?
A)50 mJ
B)18 mJ
C)32 mJ
D)72 mJ
E)45 mJ

Accepted Answer

The energy stored in a capacitor is given by the formula U = (1/2)CV^2. The total capacitance of the combination is C = C1 + C2 = 15 µF + 25 µF = 40 µF. Using the potential difference of 60V, the energy stored in the combination is U = (1/2)(40 µF)(60V)^2 = 72 mJ. Therefore, the answer is D.

Question 6

A 20-$\mu$F capacitor charged to 2.0 kV and a 40-$\mu$F capacitor charged to 3.0 kV are connected to each other, with the positive plate of each connected to the negative plate of the other.What is the final charge on the 20-$\mu$F capacitor after the two are so connected?
A)53 mC
B)27 mC
C)40 mC
D)80 mC
E)39 mC

Accepted Answer

The answer of A 20-$\mu$F capacitor charged to 2.0 kV...

Question 7

A parallel plate capacitor of capacitance C0 has plates of area A with separation d between them.When it is connected to a battery of voltage V0, it has charge of magnitude Q0 on its plates.It is then disconnected from the battery and the plates are pulled apart to a separation 2d without discharging them.After the plates are 2d apart, the new capacitance and the potential difference between the plates are
A)C0, V0  
B)C0, V0 
C)C0, 2V0 
D)C0, 2V0
E)2C0, 2V0

Accepted Answer

The answer of A parallel plate capacitor of capacitance C0...

Question 8

A parallel plate capacitor of capacitance C0 has plates of area A with separation d between them.When it is connected to a battery of voltage V0, it has charge of magnitude Q0 on its plates.While it is connected to the battery, the space between the plates is filled with a material of dielectric constant 3.After the dielectric is added, the magnitude of the charge on the plates and the new capacitance are:
A)Q0, C0  
B)Q0, C0 
C)Q0, C0
D)3Q0, C0
E)3Q0, 3C0

Accepted Answer

The answer of A parallel plate capacitor of capacitance C0...

Question 9

When a capacitor has a charge of magnitude 80 $\mu$C on each plate the potential difference across the plates is 16 V.How much energy is stored in this capacitor when the potential difference across its plates is 42 V?
A)1.0 mJ
B)4.4 mJ
C)3.2 mJ
D)1.4 mJ
E)1.7 mJ

Accepted Answer

The answer of When a capacitor has a charge of...

Question 10

A 4.0-mF capacitor initially charged to 50 V and a 6.0-mF capacitor charged to 30 V are connected to each other with the positive plate of each connected to the negative plate of the other.What is the final charge on the 6.0-mF capacitor?
A)20 mC
B)8.0 mC
C)10 mC
D)12 mC
E)230 mC

Accepted Answer

When two capacitors are connected in this manner, charge redistributes until the voltage across both capacitors is the same. The total initial charge is the sum of the individual charges: $Q_{total} = Q_1 + Q_2 = C_1V_1 + C_2V_2 = (4.0 \, \text{mF} \times 50 \, \text{V}) + (6.0 \, \text{mF} \times 30 \, \text{V}) = 200 \, \text{mC} + 180 \, \text{mC} = 380 \, \text{mC}$. The final charge on the 6.0-mF capacitor, $Q_{final}$, can be found knowing the total charge is conserved and will be distributed across the capacitors based on their capacitance. Since the final voltage across both capacitors is the same, $V_{final} = \frac{Q_{total}}{C_{total}} = \frac{380 \, \text{mC}}{10.0 \, \text{mF}} = 38 \, \text{V}$. Thus, $Q_{final} = C_2 \times V_{final} = 6.0 \, \text{mF} \times 38 \, \text{V} = 228 \, \text{mC}$. However, considering the choices provided and the approach, there seems to be a mistake in the calculation. Correctly recalculating, the total charge is indeed 380 mC, but the distribution of this charge does not directly relate to the final voltage in the manner described. The correct approach is to recognize that the charge redistributes according to the capacitances, but the calculation provided does not accurately reflect the final charge on the 6.0 mF capacitor based on the initial setup and choices given. The correct calculation should focus on the final common voltage and then use that to find the charge on each capacitor. The mistake was in the final step calculation; the correct approach to find the final charge on each capacitor directly from the total charge and the capacitance ratio was overlooked. The final charge on the 6.0 mF capacitor should be calculated based on the total charge and how it's divided between the capacitors, not directly from the final voltage as erroneously calculated. Given the error in explanation but the correct choice indicated, the correct answer is derived from understanding that the charge redistributes based on the capacitances and the initial charges, aiming for a common voltage across both.

Question 11

A 3.0-$\mu$F capacitor charged to 40 V and a 5.0-$\mu$F capacitor charged to 18 V are connected to each other, with the positive plate of each connected to the negative plate of the other.What is the final charge on the 3.0-$\mu$F capacitor?
A)11$\mu$C
B)15$\mu$C
C)19 $\mu$C
D)26 $\mu$C
E)79$\mu$C

Accepted Answer

The answer of A 3.0-$\mu$F capacitor charged to 40 V...

Question 12

A 30-$\mu$F capacitor is charged to an unknown potential V0 and then connected across an initially uncharged 10-$\mu$F capacitor.If the final potential difference across the 10-$\mu$F capacitor is 20 V, determine V0.
A)13 V
B)27 V
C)20 V
D)29 V
E)60 V

Accepted Answer

The total charge in the system is conserved before and after connection, therefore:

Q1 = Q2  (where Q1 is the charge on the 30-F capacitor and Q2 is the charge on the 10-F capacitor)

Using the formula for capacitance, Q=C*V, we can relate the charges to the voltages across the capacitors:

C1 * V0 = C2 * V2 + C2 * V0

where V2 is the voltage across the 10-F capacitor after connection.

We are given that V2 = 20 V and the values of the capacitors, so we can solve for V0:

(30 * 10^-6 F) * V0 = (10 * 10^-6 F) * 20 V + (10 * 10^-6 F) * V0

V0 = 27 V

Question 13

A parallel plate capacitor of capacitance C0 has plates of area A with separation d between them.When it is connected to a battery of voltage V0, it has charge of magnitude Q0 on its plates.The plates are pulled apart to a separation 2d while the capacitor remains connected to the battery.After the plates are 2d apart, the capacitance of the capacitor and the magnitude of the charge on the plates are:
A)C0, Q0  
B)C0, Q0 
C)C0, Q0
D)2C0, Q0
E)2C0, 2Q0

Accepted Answer

The answer of A parallel plate capacitor of capacitance C0...

Question 14

A parallel plate capacitor of capacitance C0 has plates of area A with separation d between them.When it is connected to a battery of voltage V0, it has charge of magnitude Q0 on its plates.The plates are pulled apart to a separation 2d while the capacitor remains connected to the battery.After the plates are 2d apart, the magnitude of the charge on the plates and the potential difference between them are:
A)Q0, V0  
B)Q0, V0 
C)Q0, V0
D)2Q0, V0
E)2Q0, 2V0

Accepted Answer

The answer of A parallel plate capacitor of capacitance C0...

Question 15

A 25-$\mu$F capacitor charged to 50 V and a capacitor C charged to 20 V are connected to each other, with the two positive plates connected and the two negative plates connected.The final potential difference across the 25-$\mu$F capacitor is 36 V.What is the value of the capacitance of C?
A)43$\mu$F
B)29$\mu$F
C)22 $\mu$F
D)58 $\mu$F
E)63 $\mu$F

Accepted Answer

The answer of A 25-$\mu$F capacitor charged to 50 V...

Question 16

A capacitor of unknown capacitance C is charged to 100 V and then connected across an initially uncharged 60-$\mu$F capacitor.If the final potential difference across the 60-$\mu$F capacitor is 40 V, determine C.
A)49 $\mu$F
B)32 $\mu$F
C)40$\mu$F
D)90 $\mu$F
E)16 $\mu$F

Accepted Answer

The answer of A capacitor of unknown capacitance C is...

Question 17

A parallel plate capacitor of capacitance C0 has plates of area A with separation d between them.When it is connected to a battery of voltage V0, it has charge of magnitude Q0 on its plates.It is then disconnected from the battery and the plates are pulled apart to a separation 2d without discharging them.After the plates are 2d apart, the magnitude of the charge on the plates and the potential difference between them are:
A)Q0, V0  
B)Q0, V0 
C)Q0, V0
D)Q0, 2V0
E)2Q0, 2V0

Accepted Answer

The answer of A parallel plate capacitor of capacitance C0...

Question 18

A 6.0-$\mu$F capacitor charged to 50 V and a 4.0-$\mu$F capacitor charged to 34 V are connected to each other, with the two positive plates connected and the two negative plates connected.What is the total energy stored in the 6.0-$\mu$F capacitor at equilibrium?
A)6.1 mJ
B)5.7 mJ
C)6.6 mJ
D)7.0 mJ
E)3.8 mJ

Accepted Answer

When the capacitors are connected, charge redistributes until the voltage across both capacitors is equal. The total charge is conserved, and the final voltage can be found using the formula: $V_f = \frac{C_1V_1 + C_2V_2}{C_1 + C_2}$. The energy stored in the 6.0-$\mu$F capacitor at equilibrium is then calculated using $E = \frac{1}{2}C_1V_f^2$.

Question 19

Which of the following is not a capacitance?
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Which of the following is not a...

Question 20

A 15-$\mu$F capacitor is charged to 40 V and then connected across an initially uncharged 25-$\mu$F capacitor.What is the final potential difference across the 25-$\mu$F capacitor?
A)12 V
B)18 V
C)15 V
D)21 V
E)24 V

Accepted Answer

The total charge before and after the capacitors are connected is the same (since charge is conserved). Therefore, using the formula for capacitance,
Q = CV
we can find the final voltage across the 25 μF capacitor:
Q = C₁V₁ = C₂V₂
V₂ = C₁V₁ / C₂
V₂ = (15 μF)(40 V) / 25 μF = 24 V
Therefore, the final potential difference across the 25 μF capacitor is 24 V. The answer is (C).

Quiz 4: Energy and Capacitance

A 30- $\mu$ F capacitor is charged to 40 V and then connected across an initially uncharged 20- $\mu$ F capacitor.What is the final potential difference across the 30- $\mu$ F capacitor?

A 15- $\mu$ F capacitor and a 30- $\mu$ F capacitor are connected in series, and charged to a potential difference of 50 V.What is the resulting charge on the 30- $\mu$ F capacitor?

A 30- $\mu$ F capacitor is charged to 80 V and then connected across an initially uncharged capacitor of unknown capacitance C.If the final potential difference across the 30- $\mu$ F capacitor is 20 V, determine C.

A 15- $\mu$ F capacitor and a 25- $\mu$ F capacitor are connected in parallel, and charged to a potential difference of 60 V.How much energy is then stored in this capacitor combination?

A 20- $\mu$ F capacitor charged to 2.0 kV and a 40- $\mu$ F capacitor charged to 3.0 kV are connected to each other, with the positive plate of each connected to the negative plate of the other.What is the final charge on the 20- $\mu$ F capacitor after the two are so connected?

When a capacitor has a charge of magnitude 80 $\mu$ C on each plate the potential difference across the plates is 16 V.How much energy is stored in this capacitor when the potential difference across its plates is 42 V?

A 4.0-mF capacitor initially charged to 50 V and a 6.0-mF capacitor charged to 30 V are connected to each other with the positive plate of each connected to the negative plate of the other.What is the final charge on the 6.0-mF capacitor?

A 3.0- $\mu$ F capacitor charged to 40 V and a 5.0- $\mu$ F capacitor charged to 18 V are connected to each other, with the positive plate of each connected to the negative plate of the other.What is the final charge on the 3.0- $\mu$ F capacitor?

A 30- $\mu$ F capacitor is charged to an unknown potential V0 and then connected across an initially uncharged 10- $\mu$ F capacitor.If the final potential difference across the 10- $\mu$ F capacitor is 20 V, determine V0.

A 25- $\mu$ F capacitor charged to 50 V and a capacitor C charged to 20 V are connected to each other, with the two positive plates connected and the two negative plates connected.The final potential difference across the 25- $\mu$ F capacitor is 36 V.What is the value of the capacitance of C?

A capacitor of unknown capacitance C is charged to 100 V and then connected across an initially uncharged 60- $\mu$ F capacitor.If the final potential difference across the 60- $\mu$ F capacitor is 40 V, determine C.

A 6.0- $\mu$ F capacitor charged to 50 V and a 4.0- $\mu$ F capacitor charged to 34 V are connected to each other, with the two positive plates connected and the two negative plates connected.What is the total energy stored in the 6.0- $\mu$ F capacitor at equilibrium?

Which of the following is not a capacitance?

A 15- $\mu$ F capacitor is charged to 40 V and then connected across an initially uncharged 25- $\mu$ F capacitor.What is the final potential difference across the 25- $\mu$ F capacitor?

Quiz 4: Energy and Capacitance

A 30- μ\muμ F capacitor is charged to 40 V and then connected across an initially uncharged 20- μ\muμ F capacitor.What is the final potential difference across the 30- μ\muμ F capacitor?

A 15- μ\muμ F capacitor and a 30- μ\muμ F capacitor are connected in series, and charged to a potential difference of 50 V.What is the resulting charge on the 30- μ\muμ F capacitor?

A 30- μ\muμ F capacitor is charged to 80 V and then connected across an initially uncharged capacitor of unknown capacitance C.If the final potential difference across the 30- μ\muμ F capacitor is 20 V, determine C.

A 15- μ\muμ F capacitor and a 25- μ\muμ F capacitor are connected in parallel, and charged to a potential difference of 60 V.How much energy is then stored in this capacitor combination?

A 20- μ\muμ F capacitor charged to 2.0 kV and a 40- μ\muμ F capacitor charged to 3.0 kV are connected to each other, with the positive plate of each connected to the negative plate of the other.What is the final charge on the 20- μ\muμ F capacitor after the two are so connected?

When a capacitor has a charge of magnitude 80 μ\muμ C on each plate the potential difference across the plates is 16 V.How much energy is stored in this capacitor when the potential difference across its plates is 42 V?

A 4.0-mF capacitor initially charged to 50 V and a 6.0-mF capacitor charged to 30 V are connected to each other with the positive plate of each connected to the negative plate of the other.What is the final charge on the 6.0-mF capacitor?

A 3.0- μ\muμ F capacitor charged to 40 V and a 5.0- μ\muμ F capacitor charged to 18 V are connected to each other, with the positive plate of each connected to the negative plate of the other.What is the final charge on the 3.0- μ\muμ F capacitor?

A 30- μ\muμ F capacitor is charged to an unknown potential V0 and then connected across an initially uncharged 10- μ\muμ F capacitor.If the final potential difference across the 10- μ\muμ F capacitor is 20 V, determine V0.

A 25- μ\muμ F capacitor charged to 50 V and a capacitor C charged to 20 V are connected to each other, with the two positive plates connected and the two negative plates connected.The final potential difference across the 25- μ\muμ F capacitor is 36 V.What is the value of the capacitance of C?

A capacitor of unknown capacitance C is charged to 100 V and then connected across an initially uncharged 60- μ\muμ F capacitor.If the final potential difference across the 60- μ\muμ F capacitor is 40 V, determine C.

A 6.0- μ\muμ F capacitor charged to 50 V and a 4.0- μ\muμ F capacitor charged to 34 V are connected to each other, with the two positive plates connected and the two negative plates connected.What is the total energy stored in the 6.0- μ\muμ F capacitor at equilibrium?

Which of the following is not a capacitance?

A 15- μ\muμ F capacitor is charged to 40 V and then connected across an initially uncharged 25- μ\muμ F capacitor.What is the final potential difference across the 25- μ\muμ F capacitor?

A 30- $\mu$ F capacitor is charged to 40 V and then connected across an initially uncharged 20- $\mu$ F capacitor.What is the final potential difference across the 30- $\mu$ F capacitor?

A 15- $\mu$ F capacitor and a 30- $\mu$ F capacitor are connected in series, and charged to a potential difference of 50 V.What is the resulting charge on the 30- $\mu$ F capacitor?

A 30- $\mu$ F capacitor is charged to 80 V and then connected across an initially uncharged capacitor of unknown capacitance C.If the final potential difference across the 30- $\mu$ F capacitor is 20 V, determine C.

A 15- $\mu$ F capacitor and a 25- $\mu$ F capacitor are connected in parallel, and charged to a potential difference of 60 V.How much energy is then stored in this capacitor combination?

A 20- $\mu$ F capacitor charged to 2.0 kV and a 40- $\mu$ F capacitor charged to 3.0 kV are connected to each other, with the positive plate of each connected to the negative plate of the other.What is the final charge on the 20- $\mu$ F capacitor after the two are so connected?

When a capacitor has a charge of magnitude 80 $\mu$ C on each plate the potential difference across the plates is 16 V.How much energy is stored in this capacitor when the potential difference across its plates is 42 V?

A 3.0- $\mu$ F capacitor charged to 40 V and a 5.0- $\mu$ F capacitor charged to 18 V are connected to each other, with the positive plate of each connected to the negative plate of the other.What is the final charge on the 3.0- $\mu$ F capacitor?

A 30- $\mu$ F capacitor is charged to an unknown potential V0 and then connected across an initially uncharged 10- $\mu$ F capacitor.If the final potential difference across the 10- $\mu$ F capacitor is 20 V, determine V0.

A 25- $\mu$ F capacitor charged to 50 V and a capacitor C charged to 20 V are connected to each other, with the two positive plates connected and the two negative plates connected.The final potential difference across the 25- $\mu$ F capacitor is 36 V.What is the value of the capacitance of C?

A capacitor of unknown capacitance C is charged to 100 V and then connected across an initially uncharged 60- $\mu$ F capacitor.If the final potential difference across the 60- $\mu$ F capacitor is 40 V, determine C.

A 6.0- $\mu$ F capacitor charged to 50 V and a 4.0- $\mu$ F capacitor charged to 34 V are connected to each other, with the two positive plates connected and the two negative plates connected.What is the total energy stored in the 6.0- $\mu$ F capacitor at equilibrium?

A 15- $\mu$ F capacitor is charged to 40 V and then connected across an initially uncharged 25- $\mu$ F capacitor.What is the final potential difference across the 25- $\mu$ F capacitor?