Question 1

Each of the three 25-$\mu$F capacitors shown is initially uncharged. How many coulombs of charge pass through the ammeter A after the switch S is closed? 
A) 0.033 C
B) 0.10 C
C) 0.30 C
D) 10 C
E) none of these

Accepted Answer

The answer of Each of the three 25-$\mu$F capacitors shown...

Question 2

Capacitors C₁ and C₂ are connected in series and a potential difference is applied to the combination. If the capacitor that is equivalent to the combination has the same potential difference, then the charge on the equivalent capacitor is the same as: A) the charge on C₁ B) the sum of the charges on C₁ and C₂ C) the difference of the charges on C₁ and C₂ D) the product of the charges on C₁ and C₂ E) none of the above

Accepted Answer

When capacitors are connected in series, the charge on each capacitor is the same. Therefore, the charge on the equivalent capacitor is the same as the charge on each individual capacitor in the series.

Question 3

A parallel-plate capacitor has a plate area of 0.3 m² and a plate separation of 0.1 mm. If the charge on each plate has a magnitude of 5 *10^-6 C then the force exerted by one plate on the other has a magnitude of about: A) 5 N B) 9 N C) 1 *10⁴ N D) 9 * 10⁵ N E) 2 * 10⁷ N

Accepted Answer

The answer of A parallel-plate capacitor has a plate area...

Question 4

Capacitors C₁ and C₂ are connected in parallel and a potential difference is applied to the combination. If the capacitor that is equivalent to the combination has the same potential difference, then the charge on the equivalent capacitor is the same as: A) the charge on C₁ B) the sum of the charges on C₁ and C₂ C) the difference of the charges on C₁ and C₂ D) the product of the charges on C₁ and C₂ E) none of the above

Accepted Answer

When capacitors are connected in parallel, the potential difference across each capacitor is the same. Therefore, the charge on each capacitor is determined by Q = CV, where C is the capacitance and V is the potential difference. Since the potential difference is the same for both capacitors, the charges on the capacitors are proportional to their capacitances. When they are combined, the equivalent capacitance is the sum of the individual capacitances, so the total charge is the sum of the charges on the individual capacitors. Therefore, the answer is B.

Question 5

Capacitor C₁ is connected alone to a battery and charged until the magnitude of the charge on each plate is 4.0 * 10 ^- ⁸C. Then it is removed from the battery and connected to two other capacitors C₂and C₃, as shown. The charge on the positive plate of C₁ is then 1.0 * 10 ^- ⁸C. The charges on the positive plates of C₂ and C₃are: A) q₂ = 3.0 *10 ^- ^-8C and q₃ = 3.0 *10 1^- ⁸C B) q₂ = 2.0* 10 ^- ⁸ C and q₃ = 2.0 *10 ^- 0⁸C C) q₂ = 5.0 *10 ^- ⁸ C and q₃ = 1.0 * 10 ^- ⁸C D) q₂ = 3.0 * 10 ^- ⁸C and q₃ = 1.0 *10 ^- ⁸C E) q₂ = 1.0 *10 ^- ⁸ C and q₃ = 3.0 *10 ^- ⁸C

Accepted Answer

The answer of Capacitor C₁ is connected alone to a...

Question 6

Each of the four capacitors shown is 500 $\mu$F. The voltmeter reads 1000V. The magnitude of the charge on each capacitor plate is: 
A) 0.2 C
B) 0.5 C
C) 20 C
D) 50 C
E) none of these

Accepted Answer

The total capacitance of the circuit is 500 + 500 + 500 + 10 = 1510μF. The charge on each capacitor plate is equal to the capacitance multiplied by the voltage, so the charge on each plate is 1510μF × 1000V = 1.51mC. Since there are two plates per capacitor, the total charge on each capacitor is 2 × 1.51mC = 3.02mC, which is equal to 0.5C when converted to coulombs. Therefore, the correct answer is B.

Question 7

Two identical capacitors, each with capacitance C, are connected in parallel and the combination is connected in series to a third identical capacitor. The equivalent capacitance of this arrangement is:
A) 2C/3
B) C
C) 3C/2
D) 2C
E) 3C

Accepted Answer

The answer of Two identical capacitors, each with capacitance C,...

Question 8

A 2-$\mu$F and a 1-$\mu$F capacitor are connected in series and charged from a battery. They store charges P and Q, respectively. When disconnected and charged separately using the same battery, they have charges R and S, respectively. Then:
A) R > S > Q = P
B) P > Q > R = S
C) R > P = Q > S
D) R = P > S = Q
E) R > P > S = Q

Accepted Answer

When capacitors are connected in series, the charge on them is the same. Let's assume the charge on both capacitors is x when they are connected in series and charged from the battery. Then, using the formula Q=CV, we can calculate the capacitance of 2-F1F1F1S1F1F1F10F capacitor as:
Q=x= C1V1
C1= x/V1
Similarly, the capacitance of 1-F1F1F1S1F1F1F10F capacitor can be calculated as:
Q=x= C2V2
C2= x/V2
When the capacitors are disconnected and charged separately using the same battery, their capacitance will remain the same. Let's assume the voltage across both capacitors is y. Then, the charges on them can be calculated as:
R= C1y
S= C2y
Substituting C1 and C2 from above equations, we can write:
R= (x/V1)y
S= (x/V2)y
Since V1>V2, y is larger for the 2-F1F1F1S1F1F1F10F capacitor than the 1-F1F1F1S1F1F1F10F capacitor. Therefore, R> S. 
Also, since both capacitors are charged using the same battery, the total charge on them should be the same. Hence, we can write:
P+Q=x
R+S=x
Since R>S, P+Q>x/2. Therefore, Q>P. 
Combining the above results, we get:
R>S>Q>P, which is equivalent to option A.

Question 9

A 2-$\mu$F and a 1-$\mu$F capacitor are connected in parallel and a potential difference is applied across the combination. The 2-$\mu$F capacitor has:
A) twice the charge of the 1-$\mu$F capacitor
B) half the charge of the 1-$\mu$F capacitor
C) twice the potential difference of the 1-$\mu$F capacitor
D) half the potential difference of the 1-$\mu$F capacitor
E) none of the above

Accepted Answer

When capacitors are connected in parallel, the potential difference across each capacitor is the same. Therefore, the charge on each capacitor is directly proportional to its capacitance. Since the capacitance of the 2-F1F1F1S1F1F1F10F capacitor is twice that of the 1-F1F1F1S1F1F1F10F capacitor, it will have twice the charge of the smaller capacitor.

Question 10

Two parallel-plate capacitors with the same plate area but different capacitance are connected in parallel to a battery. Both capacitors are filled with air. The quantity that is the same for both capacitors when they are fully charged is:
A) potential difference
B) energy density
C) electric field between the plates
D) charge on the positive plate
E) plate separation

Accepted Answer

When two capacitors are connected in parallel, the potential difference across both capacitors is the same because they are connected to the same battery. Therefore, choice A is the correct answer. The energy density, electric field between the plates, charge on the positive plate, and plate separation can all be different for the two capacitors, so they are not the same for both capacitors.

Question 11

Capacitors C₁ and C₂ are connected in series. The equivalent capacitance is given by: A) C₁C₂/(C₁ + C₂) B) (C₁ + C₂)/C₁C₂ C) 1/(C₁ + C₂) D) C₁/C₂ E) C₁ + C₂

Accepted Answer

When capacitors are connected in series, their equivalent capacitance is given by the formula: C_eq = (C_1*C_2)/(C_1+C_2) Applying this formula to the given capacitors C₁ and C₂, we get: C_eq = (C₁*C₂)/(C₁+C₂) Hence, the correct answer is A.

Question 12

Two parallel-plate capacitors with the same plate separation but different capacitance are connected in parallel to a battery. Both capacitors are filled with air. The quantity that is NOT the same for both capacitors when they are fully charged is:
A) potential difference
B) energy density
C) electric field between the plates
D) charge on the positive plate
E) dielectric constant

Accepted Answer

The answer of Two parallel-plate capacitors with the same plate...

Question 13

Two identical capacitors are connected in series and two, each identical to the first, are connected in parallel. The equivalent capacitance of the series connection is ________ the equivalent capacitance of parallel connection.
A) twice
B) four times
C) half
D) one fourth
E) the same as

Accepted Answer

The answer of Two identical capacitors are connected in series...

Question 14

Two parallel-plate capacitors with different capacitance but the same plate separation are connected in series to a battery. Both capacitors are filled with air. The quantity that is the same for both capacitors when they are fully charged is:
A) potential difference
B) stored energy
C) energy density
D) electric field between the plates
E) charge on the positive plate

Accepted Answer

When two capacitors are connected in series to a battery, the charge on the positive plate of both capacitors is the same. This is because the charge must be conserved and what flows into one capacitor must flow out and into the next in a series circuit.

Question 15

A battery is used to charge a series combination of two identical capacitors. If the potential difference across the battery terminals is V and total charge Q flows through the battery during the charging process then the charge on the positive plate of each capacitor and the potential difference across each capacitor are:
A) Q/2 and V/2, respectively
B) Q and V, respectively
C) Q/2 and V, respectively
D) Q and V/2, respectively
E) Q and 2V, respectively

Accepted Answer

The answer of A battery is used to charge a...

Question 16

Two parallel-plate capacitors with different plate separation but the same capacitance are connected in series to a battery. Both capacitors are filled with air. The quantity that is NOT the same for both capacitors when they are fully charged is:
A) potential difference
B) stored energy
C) electric field between the plates
D) charge on the positive plate
E) dielectric constant

Accepted Answer

The answer of Two parallel-plate capacitors with different plate separation...

Question 17

The diagram shows six 6-$\mu$F capacitors. The capacitance between points a and b is: 
A) 1 $\mu$F
B) 3 $\mu$F
C) 4 $\mu$F
D) 6 $\mu$F
E) 9 $\mu$F

Accepted Answer

To find the capacitance between points a and b, we need to first identify the capacitors that are in parallel and then add them up.

Starting with the bottom row, the two 1F1F1S1F1F1F10F capacitors are in parallel, so their total capacitance is 2F1F1F1S1F1F1F10F.

Moving up to the second row, we have a 6F1F1F1S1F1F1F10F capacitor, which is not directly in parallel with any other capacitors. However, if we look at the top row, we see that the 6F1F1F1S1F1F1F10F capacitor is in parallel with the 1F1F1S1F1F1F10F capacitor on the left. So we can combine these two capacitors to get a total capacitance of 7F1F1F1S1F1F1F10F.

Finally, we have the 1F1F1S1F1F1F10F capacitor on the right in the top row, which is not in parallel with any other capacitors.

To get the total capacitance between points a and b, we add up the capacitors that are in parallel:

2F1F1F1S1F1F1F10F + 7F1F1F1S1F1F1F10F + 1F1F1S1F1F1F10F = 10F1F1F1S1F1F1F10F

Therefore, the best choice is C) 4 F1F1F1S1F1F1F10F.

Question 18

A 2-$\mu$F and a 1-$\mu$F capacitor are connected in series and a potential difference is applied across the combination. The 2-$\mu$F capacitor has:
A) twice the charge of the 1-$\mu$F capacitor
B) half the charge of the 1-$\mu$F capacitor
C) twice the potential difference of the 1-$\mu$F capacitor
D) half the potential difference of the 1-$\mu$F capacitor
E) none of the above

Accepted Answer

When capacitors are connected in series, the potential difference across each capacitor is proportional to its capacitance. Since the 2-F1F1F1S1F1F1F10F capacitor has twice the capacitance of the 1-F1F1F1S1F1F1F10F capacitor, it will have half the potential difference across it. Therefore, option D is correct. The charge on each capacitor will be different, but we don't have enough information to determine the exact ratio, so options A and B are not correct. Option C is also not correct because the potential difference across a capacitor is directly proportional to its capacitance, not inversely proportional.

Question 19

A battery is used to charge a parallel combination of two identical capacitors. If the potential difference across the battery terminals is V and the total charge Q flows through the battery during the charging process then the charge on the positive plate of each capacitor and the potential difference across each capacitor are:
A) Q/2 and V/2, respectively
B) Q and V, respectively
C) Q/2 and V, respectively
D) Q and V/2, respectively
E) Q and 2V, respectively

Accepted Answer

In a parallel combination of capacitors, the potential difference across each capacitor is the same and equal to the voltage of the battery, V. The charge on each capacitor is Q/2, as the total charge Q is shared equally between the two capacitors. Therefore, the correct choice is C, where the charge on the positive plate of each capacitor is Q/2 and the potential difference across each capacitor is V.

Question 20

Capacitor C₁ and C₂ are connected in parallel. The equivalent capacitance is given by: A) C₁C₂/(C₁ + C₂) B) (C₁ + C₂)/C₁C₂ C) 1/(C₁ + C₂) D) C₁/C₂ E) C₁ + C₂

Accepted Answer

When capacitors are connected in parallel, their equivalent capacitance is the sum of their individual capacitances.

Quiz 25: Capacitance

Capacitors C₁ and C₂ are connected in series and a potential difference is applied to the combination. If the capacitor that is equivalent to the combination has the same potential difference, then the charge on the equivalent capacitor is the same as:

A parallel-plate capacitor has a plate area of 0.3 m² and a plate separation of 0.1 mm. If the charge on each plate has a magnitude of 5 *10^-6 C then the force exerted by one plate on the other has a magnitude of about:

Capacitors C₁ and C₂ are connected in parallel and a potential difference is applied to the combination. If the capacitor that is equivalent to the combination has the same potential difference, then the charge on the equivalent capacitor is the same as:

Two identical capacitors, each with capacitance C, are connected in parallel and the combination is connected in series to a third identical capacitor. The equivalent capacitance of this arrangement is:

A 2- $\mu$ F and a 1- $\mu$ F capacitor are connected in series and charged from a battery. They store charges P and Q, respectively. When disconnected and charged separately using the same battery, they have charges R and S, respectively. Then:

A 2- $\mu$ F and a 1- $\mu$ F capacitor are connected in parallel and a potential difference is applied across the combination. The 2- $\mu$ F capacitor has:

Two parallel-plate capacitors with the same plate area but different capacitance are connected in parallel to a battery. Both capacitors are filled with air. The quantity that is the same for both capacitors when they are fully charged is:

Capacitors C₁ and C₂ are connected in series. The equivalent capacitance is given by:

Two parallel-plate capacitors with the same plate separation but different capacitance are connected in parallel to a battery. Both capacitors are filled with air. The quantity that is NOT the same for both capacitors when they are fully charged is:

Two identical capacitors are connected in series and two, each identical to the first, are connected in parallel. The equivalent capacitance of the series connection is ________ the equivalent capacitance of parallel connection.

Two parallel-plate capacitors with different capacitance but the same plate separation are connected in series to a battery. Both capacitors are filled with air. The quantity that is the same for both capacitors when they are fully charged is:

Two parallel-plate capacitors with different plate separation but the same capacitance are connected in series to a battery. Both capacitors are filled with air. The quantity that is NOT the same for both capacitors when they are fully charged is:

The diagram shows six 6- $\mu$ F capacitors. The capacitance between points a and b is: $The diagram shows six 6- \mu F capacitors. The capacitance between points a and b is: A) 1 \mu F B) 3 \mu F C) 4 \mu F D) 6 \mu F E) 9 \mu F$

A 2- $\mu$ F and a 1- $\mu$ F capacitor are connected in series and a potential difference is applied across the combination. The 2- $\mu$ F capacitor has:

Capacitor C₁ and C₂ are connected in parallel. The equivalent capacitance is given by:

Quiz 25: Capacitance

Each of the three 25- μ\muμ F capacitors shown is initially uncharged. How many coulombs of charge pass through the ammeter A after the switch S is closed?

Capacitors C1 and C2 are connected in series and a potential difference is applied to the combination. If the capacitor that is equivalent to the combination has the same potential difference, then the charge on the equivalent capacitor is the same as:

A parallel-plate capacitor has a plate area of 0.3 m2 and a plate separation of 0.1 mm. If the charge on each plate has a magnitude of 5 *10-6 C then the force exerted by one plate on the other has a magnitude of about:

Capacitors C1 and C2 are connected in parallel and a potential difference is applied to the combination. If the capacitor that is equivalent to the combination has the same potential difference, then the charge on the equivalent capacitor is the same as:

Each of the four capacitors shown is 500 μ\muμ F. The voltmeter reads 1000V. The magnitude of the charge on each capacitor plate is: