Question 1

Four identical 4-mF capacitors are connected together electrically. What is the greatest possible capacitance of the combination?

Accepted Answer

When identical capacitors are connected in parallel, their capacitances add. So, the greatest possible capacitance is achieved when all four capacitors are connected in parallel. In this case, the total capacitance is:C = C1 + C2 + C3 + C4= 4 mF + 4 mF + 4 mF + 4 mF= 16 mFTherefore, the greatest possible capacitance is 16 mF.

Question 2

If C₁= 25 µF, C₂ = 20 µF, C₃ = 10 µF, and $\Delta$V₀ = 42 V, determine the energy stored by C₃.

Accepted Answer

The answer of If C₁= 25 µF, C₂ =...

Question 3

What is the equivalent capacitance of the combination shown?

Accepted Answer

The answer of What is the equivalent capacitance of the...

Question 4

Four identical 4-mF capacitors are connected together electrically. What is the least possible capacitance of the combination?

Accepted Answer

The answer of Four identical 4-mF capacitors are connected together...

Question 5

How much charge can be placed on a capacitor of plate area 20 cm² with air between the plates before it reaches "atmospheric breakdown" where E = 3.0 *10⁶ V/m? ($\varepsilon$₀ = 8.85 *10^-¹² C²/N.m²)

Accepted Answer

The answer of How much charge can be placed on...

Question 6

Two capacitors with capacitances of 1.0 $\mu$F and 0.50 $\mu$F, respectively, are connected in series. The system is connected to a 50-V battery. What electrical potential energy is stored in the 1.0-$\mu$F capacitor?

Accepted Answer

When capacitors are connected in series, the charge on each capacitor is the same. The equivalent capacitance (C_eq) for capacitors in series is given by 1/C_eq = 1/C1 + 1/C2. For the given capacitors, C_eq = 0.333 μF. The voltage across the 1.0 μF capacitor can be found using the charge (Q = C_eq * V_battery) and the relation Q = C * V. The energy stored in a capacitor is given by U = 0.5 * C * V^2. Calculating this for the 1.0 μF capacitor gives approximately 1.4 x 10^-4 J.

Question 7

Capacitor #1 has parallel plates of length L and width W, plate separation d, and is filled with dielectric with constant  .Capacitor #2 has parallel plates of length 2L and width 2W, plate separation 2d, and is filled with dielectric with constant 2  . If a voltage V is applied to capacitor #1 and a voltage 2V is applied to capacitor #2, which capacitor stores more energy and by what factor?

Accepted Answer

The answer of Capacitor #1 has parallel plates of length...

Question 8

A 6.0-$\mu$F capacitor is attached to a 20-V power supply. How much energy is stored in the capacitor?

Accepted Answer

The answer of A 6.0-$\mu$F capacitor is attached to a...

Question 9

What is the equivalent capacitance of the combination shown?

Accepted Answer

The answer of What is the equivalent capacitance of the...

Question 10

Two capacitors with capacitances of 1.5 $\mu$F and 0.25 $\mu$F, respectively, are connected in parallel. The system is connected to a 100-V battery. What electrical potential energy is stored in the 1.5-$\mu$F capacitor?

Accepted Answer

The energy stored in a capacitor is given by the formula $ E = \frac{1}{2} C V^2 $. For the 1.5 μF capacitor connected to a 100 V battery, $ E = \frac{1}{2} \times 1.5 \times 10^{-6} \times (100)^2 = 7.5 \times 10^{-3} $ J.

Question 11

A parallel plate capacitor has the voltage applied to it doubled. Is the force between the plates attractive or repulsive, and what happens to the force between the plates when the voltage is doubled?

Accepted Answer

The answer of A parallel plate capacitor has the voltage...

Question 12

If C = 14 µF, what is the equivalent capacitance for the combination shown?

Accepted Answer

The answer of If C = 14 µF, what is...

Question 13

A pair of parallel plates, forming a capacitor, are charged. The plates are pulled apart to triple the original separation, the charges on the plates remaining the same. What is the ratio of the final energy stored to the original energy stored?

Accepted Answer

The answer of A pair of parallel plates, forming a...

Question 14

The dielectric strength of rutile is 6.0 *10⁶ V/m, which corresponds to the maximum electric field that the dielectric can sustain before breakdown. What is the maximum charge that a 10 ^- ¹⁰-F capacitor with a 0.50-mm thickness of Rutile can hold?

Accepted Answer

The maximum charge that a capacitor can hold is given by Q = CV, where C is the capacitance and V is the voltage. The capacitance of a parallel-plate capacitor is given by C = εA/d, where ε is the permittivity of the dielectric, A is the area of the plates, and d is the distance between the plates. The dielectric strength of a material is the maximum electric field that the material can sustain before breakdown. The electric field in a capacitor is given by E = V/d. Therefore, the maximum charge that a capacitor can hold is given by:Q = CV = εAV/d = (εA/d)V = CEwhere E is the dielectric strength of the material.In this problem, the dielectric strength of rutile is 6.0 × 10^6 V/m, the thickness of the dielectric is 0.50 mm = 5.0 × 10^-4 m, and the area of the plates is not given. Therefore, we cannot calculate the maximum charge that the capacitor can hold without knowing the area of the plates. However, we can say that the maximum charge that the capacitor can hold is proportional to the area of the plates.

Question 15

A pair of parallel plates, forming a capacitor, are connected to a battery. While the capacitor is still connected to the battery maintaining a constant voltage, the plates are pulled apart to triple their original distance. What is the ratio of the final energy stored to the original energy stored?

Accepted Answer

The answer of A pair of parallel plates, forming a...

Question 16

Using a 1-mF capacitor, a 2-mF capacitor, and a 3-mF capacitor, which of the following capacitances cannot be made by a combination that uses all three? (Hint: At most only 2 combinations must be considered to determine the correct answer.)

Accepted Answer

Using all three capacitors, the total capacitance can be calculated by considering series and parallel combinations. The combination that results in 7 mF cannot be achieved with these capacitors.

Question 17

A parallel-plate capacitor has dimensions 4.0 cm * 5.0 cm. The plates are separated by a 1.0-mm thickness of paper (dielectric constant $\kappa$ = 3.7). What is the charge that can be stored on this capacitor, when connected to a 6.0-V battery? ($\varepsilon$₀ = 8.85 * 10^-¹²C²/N.m²)

Accepted Answer

The answer of A parallel-plate capacitor has dimensions 4.0 cm...

Question 18

A "sandwich" is constructed of two flat pieces of metal (2.00 cm on a side) with a 3.00-mm thick piece of a dielectric called rutile ($\kappa$ = 100) in between them. What is the capacitance? ($\varepsilon$₀ = 8.85 * 10^-¹²C²/N.m²)

Accepted Answer

The answer of A "sandwich" is constructed of two flat...

Question 19

A 0.50-$\mu$F capacitor is connected to a 400-V battery. What potential energy is stored in the capacitor?

Accepted Answer

The potential energy (U) stored in a capacitor is given by the formula U = 0.5 * C * V^2. Substituting C = 0.50 μF = 0.50 x 10^-6 F and V = 400 V, we get U = 0.5 * 0.50 x 10^-6 * 400^2 = 0.040 J.

Question 20

Inserting a dielectric material between two charged parallel conducting plates, originally separated by air and disconnected from a battery, will produce what effect on the capacitor?

Accepted Answer

Inserting a dielectric increases the capacitance of a capacitor because it reduces the electric field, allowing the capacitor to store more charge for the same voltage.

Quiz 18: Electric Potential

Four identical 4-mF capacitors are connected together electrically. What is the greatest possible capacitance of the combination?

What is the equivalent capacitance of the combination shown?

Four identical 4-mF capacitors are connected together electrically. What is the least possible capacitance of the combination?

How much charge can be placed on a capacitor of plate area 20 cm² with air between the plates before it reaches "atmospheric breakdown" where E = 3.0 10⁶ V/m? ( $\varepsilon$ ₀ = 8.85 10^-¹² C²/N.m²)

Two capacitors with capacitances of 1.0 $\mu$ F and 0.50 $\mu$ F, respectively, are connected in series. The system is connected to a 50-V battery. What electrical potential energy is stored in the 1.0- $\mu$ F capacitor?

A 6.0- $\mu$ F capacitor is attached to a 20-V power supply. How much energy is stored in the capacitor?

What is the equivalent capacitance of the combination shown?

Two capacitors with capacitances of 1.5 $\mu$ F and 0.25 $\mu$ F, respectively, are connected in parallel. The system is connected to a 100-V battery. What electrical potential energy is stored in the 1.5- $\mu$ F capacitor?

A parallel plate capacitor has the voltage applied to it doubled. Is the force between the plates attractive or repulsive, and what happens to the force between the plates when the voltage is doubled?

If C = 14 µF, what is the equivalent capacitance for the combination shown?

A pair of parallel plates, forming a capacitor, are charged. The plates are pulled apart to triple the original separation, the charges on the plates remaining the same. What is the ratio of the final energy stored to the original energy stored?

The dielectric strength of rutile is 6.0 *10⁶ V/m, which corresponds to the maximum electric field that the dielectric can sustain before breakdown. What is the maximum charge that a 10 ^- ¹⁰-F capacitor with a 0.50-mm thickness of Rutile can hold?

A pair of parallel plates, forming a capacitor, are connected to a battery. While the capacitor is still connected to the battery maintaining a constant voltage, the plates are pulled apart to triple their original distance. What is the ratio of the final energy stored to the original energy stored?

Using a 1-mF capacitor, a 2-mF capacitor, and a 3-mF capacitor, which of the following capacitances cannot be made by a combination that uses all three? (Hint: At most only 2 combinations must be considered to determine the correct answer.)

A parallel-plate capacitor has dimensions 4.0 cm * 5.0 cm. The plates are separated by a 1.0-mm thickness of paper (dielectric constant $\kappa$ = 3.7) . What is the charge that can be stored on this capacitor, when connected to a 6.0-V battery? ( $\varepsilon$ ₀ = 8.85 * 10^-¹²C²/N.m²)

A "sandwich" is constructed of two flat pieces of metal (2.00 cm on a side) with a 3.00-mm thick piece of a dielectric called rutile ( $\kappa$ = 100) in between them. What is the capacitance? ( $\varepsilon$ ₀ = 8.85 * 10^-¹²C²/N.m²)

A 0.50- $\mu$ F capacitor is connected to a 400-V battery. What potential energy is stored in the capacitor?

Inserting a dielectric material between two charged parallel conducting plates, originally separated by air and disconnected from a battery, will produce what effect on the capacitor?

Quiz 18: Electric Potential

Four identical 4-mF capacitors are connected together electrically. What is the greatest possible capacitance of the combination?

If C1 = 25 µF, C2 = 20 µF, C3 = 10 µF, and Δ\DeltaΔ V0 = 42 V, determine the energy stored by C3.

What is the equivalent capacitance of the combination shown?

Four identical 4-mF capacitors are connected together electrically. What is the least possible capacitance of the combination?

How much charge can be placed on a capacitor of plate area 20 cm2 with air between the plates before it reaches "atmospheric breakdown" where E = 3.0 *106 V/m? ( ε\varepsilonε 0 = 8.85 *10-12 C2/N.m2)

Two capacitors with capacitances of 1.0 μ\muμ F and 0.50 μ\muμ F, respectively, are connected in series. The system is connected to a 50-V battery. What electrical potential energy is stored in the 1.0- μ\muμ F capacitor?

A 6.0- μ\muμ F capacitor is attached to a 20-V power supply. How much energy is stored in the capacitor?

What is the equivalent capacitance of the combination shown?

Two capacitors with capacitances of 1.5 μ\muμ F and 0.25 μ\muμ F, respectively, are connected in parallel. The system is connected to a 100-V battery. What electrical potential energy is stored in the 1.5- μ\muμ F capacitor?

A parallel plate capacitor has the voltage applied to it doubled. Is the force between the plates attractive or repulsive, and what happens to the force between the plates when the voltage is doubled?

If C = 14 µF, what is the equivalent capacitance for the combination shown?

A pair of parallel plates, forming a capacitor, are charged. The plates are pulled apart to triple the original separation, the charges on the plates remaining the same. What is the ratio of the final energy stored to the original energy stored?

The dielectric strength of rutile is 6.0 *106 V/m, which corresponds to the maximum electric field that the dielectric can sustain before breakdown. What is the maximum charge that a 10 - 10-F capacitor with a 0.50-mm thickness of Rutile can hold?

Using a 1-mF capacitor, a 2-mF capacitor, and a 3-mF capacitor, which of the following capacitances cannot be made by a combination that uses all three? (Hint: At most only 2 combinations must be considered to determine the correct answer.)

A parallel-plate capacitor has dimensions 4.0 cm * 5.0 cm. The plates are separated by a 1.0-mm thickness of paper (dielectric constant κ\kappaκ = 3.7) . What is the charge that can be stored on this capacitor, when connected to a 6.0-V battery? ( ε\varepsilonε 0 = 8.85 * 10-12 C2/N.m2)

A "sandwich" is constructed of two flat pieces of metal (2.00 cm on a side) with a 3.00-mm thick piece of a dielectric called rutile ( κ\kappaκ = 100) in between them. What is the capacitance? ( ε\varepsilonε 0 = 8.85 * 10-12 C2/N.m2)

A 0.50- μ\muμ F capacitor is connected to a 400-V battery. What potential energy is stored in the capacitor?

Inserting a dielectric material between two charged parallel conducting plates, originally separated by air and disconnected from a battery, will produce what effect on the capacitor?

How much charge can be placed on a capacitor of plate area 20 cm² with air between the plates before it reaches "atmospheric breakdown" where E = 3.0 10⁶ V/m? ( $\varepsilon$ ₀ = 8.85 10^-¹² C²/N.m²)

Two capacitors with capacitances of 1.0 $\mu$ F and 0.50 $\mu$ F, respectively, are connected in series. The system is connected to a 50-V battery. What electrical potential energy is stored in the 1.0- $\mu$ F capacitor?

A 6.0- $\mu$ F capacitor is attached to a 20-V power supply. How much energy is stored in the capacitor?

Two capacitors with capacitances of 1.5 $\mu$ F and 0.25 $\mu$ F, respectively, are connected in parallel. The system is connected to a 100-V battery. What electrical potential energy is stored in the 1.5- $\mu$ F capacitor?

The dielectric strength of rutile is 6.0 *10⁶ V/m, which corresponds to the maximum electric field that the dielectric can sustain before breakdown. What is the maximum charge that a 10 ^- ¹⁰-F capacitor with a 0.50-mm thickness of Rutile can hold?

A parallel-plate capacitor has dimensions 4.0 cm * 5.0 cm. The plates are separated by a 1.0-mm thickness of paper (dielectric constant $\kappa$ = 3.7) . What is the charge that can be stored on this capacitor, when connected to a 6.0-V battery? ( $\varepsilon$ ₀ = 8.85 * 10^-¹²C²/N.m²)

A "sandwich" is constructed of two flat pieces of metal (2.00 cm on a side) with a 3.00-mm thick piece of a dielectric called rutile ( $\kappa$ = 100) in between them. What is the capacitance? ( $\varepsilon$ ₀ = 8.85 * 10^-¹²C²/N.m²)

A 0.50- $\mu$ F capacitor is connected to a 400-V battery. What potential energy is stored in the capacitor?