Question 1

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

By analyzing the circuit, we can simplify it to the following equivalent circuit:
- Two parallel capacitors with capacitance 6F1F1F1S1μF1F1F10F each, resulting in an equivalent capacitance of 12F1F1F1S1μF1F1F10F.
- Two series capacitors each with capacitance 6F1F1F1S1μF1F1F10F, resulting in an equivalent capacitance of 3F1F1F1S1μF1F1F10F.
- One series capacitor with capacitance 3F1F1F1S1μF1F1F10F and one parallel capacitor with capacitance 6F1F1F1S1μF1F1F10F, resulting in an equivalent capacitance of 2F1F1F1S1μF1F1F7.5F.

Finally, the total capacitance between a and b is the sum of the equivalent capacitances obtained, which is 12F1F1F1S1μF1F1F10F + 3F1F1F1S1μF1F1F10F + 2F1F1F1S1μF1F1F7.5F = 17F1F1F1S1μF1F1F7.5F. However, none of the answer choices match this value exactly, so we choose the closest choice, which is C) 4 F1F1F1S1μF1F1F10F.

Question 2

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 given by Q = CV, where C is the capacitance and V is the potential difference. For the equivalent capacitor, the capacitance is given by Ceq = C1 + C2, where C1 and C2 are the capacitances of the individual capacitors. Therefore, the total charge on the equivalent capacitor is Qeq = Ceq * V = (C1 + C2) * V = C1 * V + C2 * V, which is equal to the sum of the charges on the individual capacitors.

Question 3

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

When capacitors are connected in series, the equivalent capacitance is less than that of a single capacitor and is given by the reciprocal formula: 1/C_eq_series = 1/C + 1/C = 1/(C/2). For parallel capacitors, the equivalent capacitance is the sum: C_eq_parallel = C + C = 2C. Therefore, the series capacitance is one fourth of the parallel capacitance.

Question 4

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 ^- ⁸C B)q₂ = 2.0 *10 ^- ⁸ C and q₃ = 2.0 *10 ^- ⁸C 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

We can use the conservation of charge in a series combination of capacitors. Since the capacitors are connected in series, the magnitude of the charge on each capacitor will be the same. Let q be the magnitude of the charge on each capacitor. Before the capacitors are connected, the charge on each plate of C₁ is 4.0 F1F1F1S1F1F1F10 10F1F1F1S1^F1F1F10⁸C. Therefore, the total charge on C₁ is 8q. After the capacitors are connected in series, the charge on the positive plate of C₁ is 1.0 F1F1F1S1F1F1F10 10F1F1F1S1^F1F1F10⁸C. Therefore, the total charge on C₁ is 2q. By conservation of charge, the total charge on C₂ and C₃ combined is 6q. Since the capacitors are in series, the charge on the positive plate of C₂ is q/3 and the charge on the positive plate of C₃ is 5q/3 (or vice versa). Therefore, the answer is (A) q₂ = 3.0 F1F1F1S1F1F1F10 10F1F1F1S1^F1F1F10^-8C and q₃ = 3.0 F1F1F1S1F1F1F10 10F1F1F1S1^F1F1F10⁸C.

Question 5

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 6

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 7

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 125µF. Using the formula Q=CV, the charge on each capacitor is Q=CV=(125x10^-6 F)x(1000V)=0.125C. Since each capacitor has two plates, the charge on each plate is half of the total charge, which is 0.125C/2=0.0625C. Therefore, the answer is closest to 0.5C, which is choice B.

Question 8

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

In a parallel-plate capacitor, the potential difference (or voltage) across the plates is the same for both capacitors, regardless of their capacitance. This is because they are connected in parallel to the same battery, which maintains a constant potential difference. The energy density, electric field between the plates, charge on the positive plate, and plate separation will all differ between the two capacitors due to their different capacitances. Therefore, the only quantity that remains the same is the potential difference.

Question 9

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 electric field between the plates is inversely proportional to the plate separation. Since the capacitors have the same capacitance but different plate separations, the electric field between the plates will be different for each capacitor.

Question 10

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 can be calculated using the formula: 1/Ceq = 1/C1 + 1/C2 + 1/C3 + ... In this case, we have two capacitors in series, so the formula becomes: 1/Ceq = 1/C₁ + 1/C₂ To get the equivalent capacitance, we need to invert both sides of the equation: Ceq = 1/(1/C₁ + 1/C₂) Simplifying this expression, we get: Ceq = C₁C₂/(C₁ + C₂) Therefore, the correct answer is A.

Question 11

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

The answer of A 2-$\mu$F and a 1-$\mu$F capacitor are...

Question 12

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 13

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 14

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 charge on each capacitor will be the same. However, the voltage across each capacitor will be different and is inversely proportional to the capacitance. Therefore, the capacitor with smaller capacitance will have a higher voltage than the capacitor with larger capacitance. In this case, the 1-F1F1F1S1F1F1F10F capacitor has smaller capacitance and will have a higher voltage than the 2-F1F1F1S1F1F1F10F capacitor. So, the 2-F1F1F1S1F1F1F10F capacitor will have half the potential difference of the 1-F1F1F1S1F1F1F10F capacitor.

Question 15

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 two identical capacitors, both capacitors have the same potential difference across them. Therefore, each capacitor has a potential difference of V. The charge on the positive plate of each capacitor is Q/2 as the capacitors are identical and the charges are shared equally between them. Therefore, the correct choice is (C) Q/2 and V, respectively.

Question 16

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 17

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

When capacitors are connected in parallel, they have the same potential difference across them, but the charge on each capacitor depends on its capacitance. Therefore, the charge on the positive plate is not the same for both capacitors.

Question 18

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.

Question 19

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 20

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.

Quiz 25: Capacitance

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

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 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.

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:

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:

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:

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

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:

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 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:

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:

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:

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

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:

Quiz 25: Capacitance

The diagram shows six 6- μ\muμ F capacitors.The capacitance between points a and b is:

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 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.

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:

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: