Question 1

A parallel-plate capacitor has a voltage V = 6.0 V between its plates. Each plate carries a surface charge density σ = 7.0 nC/m². What is the separation of the plates?

Accepted Answer

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Question 2

The capacitance per unit length of a coaxial cable, made of two concentric cylinders, is 50 pF/m. What is the radius of the outer cylinder if the radius of the inner one is 1.0 mm?

Accepted Answer

The capacitance per unit length of a coaxial cable is given by:C = (2πε)/(ln(b/a))where:C is the capacitance per unit lengthε is the permittivity of the material between the conductorsa is the radius of the inner conductorb is the radius of the outer conductorIn this problem, we are given that C = 50 pF/m and a = 1.0 mm. We can use the above equation to solve for b:50 pF/m = (2πε)/(ln(b/1.0 mm))Solving for b, we get:b = 3.0 mmTherefore, the radius of the outer cylinder is 3.0 mm.

Question 3

A parallel plate capacitor with plate separation of 4.0 cm has a plate area of 4.0 × 10^-2 m². What is the capacitance of this capacitor with air between these plates?

Accepted Answer

The capacitance of a parallel plate capacitor can be calculated using the formula:

C = εA/d

Where C is the capacitance, ε is the permittivity of the medium between the plates (in this case air, which has a value of about 8.85 × 10^-12 F/m), A is the area of the plates, and d is the distance between them.

Plugging in the given values:

C = (8.85 × 10^-12 F/m) × (4.0 × 10^-2 m^2) / 4.0 × 10^-2 m

Simplifying:

C = 8.9 × 10^-12 F

Therefore, the best choice is answer B, 8.9 × 10^-12 F.

Question 4

The magnitude of the charge on each plate of a parallel plate capacitor is 4 μC and the potential difference between the plates is 80 V. What is the capacitance of this capacitor?

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Question 5

FIGURE 24-8 
-A system of capacitors is connected across a 90 V DC voltage source as shown in Fig. 24-8. What is the equivalent capacitance of this system?

Accepted Answer

The answer of FIGURE 24-8 
-A system of capacitors is...

Question 6

A 4.0 μF and a 6.0 μF capacitor are connected in series across an 8.0-V DC source. What is the charge on the 6.0 μF capacitor?

Accepted Answer

The total capacitance in the circuit can be found using the formula

1/C_total = 1/C1 + 1/C2

Substituting the values, we get

1/C_total = 1/4 + 1/6

1/C_total = 5/12

C_total = 12/5 μF

The total charge on the capacitors is given by

Q = CV

where C is the total capacitance and V is the voltage across the capacitors.

Substituting the values, we get

Q = (12/5) x 8

Q = 96/5 μC

Since the two capacitors are in series, they have the same charge. Thus,

Q1 = Q2 = 96/5 x (6/10) = 19.2/5

Q2 = 3.84 μC

Therefore, the answer is E) 19 μC (rounded to the nearest whole number).

Question 7

FIGURE 24-6 
-Three capacitors are connected as shown in Fig. 24-6. What is the equivalent capacitance between points A and B?

Accepted Answer

The answer of FIGURE 24-6 
-Three capacitors are connected as...

Question 8

A 1 pF capacitor is connected in parallel with a 2 pF capacitor, the parallel combination then being connected in series with a 3 pF capacitor. The resulting equivalent capacitance is

Accepted Answer

The parallel combination of 1 pF and 2 pF capacitors results in a capacitance of 3 pF. This 3 pF is then in series with another 3 pF capacitor, resulting in an equivalent capacitance of 1.5 pF.

Question 9

What charge appears on the plates of a 6.0-μF capacitor when it is charged to 40 V?

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The answer of What charge appears on the plates of...

Question 10

A 2.0 μF and a 4.0 μF capacitor are connected in series across an 8.0-V DC source. What is the charge on the 2.0 μF capacitor?

Accepted Answer

The answer of A 2.0 μF and a 4.0 μF...

Question 11

The potential difference between the plates of a parallel plate capacitor is 35 V and the electric field between the plates has a strength of 750 V/m. If the plate area is 4.0 × 10^-2 m², what is the capacitance of this capacitor?

Accepted Answer

The capacitance of a parallel plate capacitor is given by $C = \frac{\epsilon_0A}{d}$, where $\epsilon_0$ is the permittivity of free space, $A$ is the area of the plates, and $d$ is the distance between the plates. We can rearrange this equation to express $d$ in terms of $C$ and $A$: $d = \frac{\epsilon_0A}{C}$. The electric field between the plates is given by $E = \frac{V}{d}$, where $V$ is the potential difference between the plates. Substituting for $d$, we have $E = \frac{V}{\frac{\epsilon_0A}{C}}$, or $C = \frac{\epsilon_0AV}{E}$. Plugging in the given values, we get $C = \frac{(8.85	imes10^{-12}	extrm{ F/m})(4.0	imes10^{-2}	extrm{ m}^2)(35	extrm{ V})}{750	extrm{ V/m}} \approx 7.6	imes10^{-12}	extrm{ F}$. The correct answer is therefore choice B.

Question 12

A parallel-plate capacitor has a plate separation of 5.0 cm. If the potential difference between the plates is 2000 V, with the top plate at the higher potential, what is the electric field between the plates?

Accepted Answer

The electric field (E) between the plates of a parallel-plate capacitor is given by the formula E = V/d, where V is the potential difference and d is the separation between the plates. Here, V = 2000 V and d = 0.05 m. Thus, E = 2000 / 0.05 = 40000 N/C. Since the top plate is at a higher potential, the electric field direction is downward.

Question 13

FIGURE 24-9 -In Fig. 24-9, three capacitors with capacitances C₁ = 4 μF, C₂ = 3μF, and C₃ = 2 μF, are connected to a battery of voltage V = 12 V. What is the charge on capacitor C₂ ?

Accepted Answer

The charge on a capacitor in a series circuit is the same for all capacitors. First, find the equivalent capacitance of the series combination: 1/C_eq = 1/C1 + 1/C2 + 1/C3 = 1/4 + 1/3 + 1/2 = 1/12. The equivalent capacitance C_eq = 12/13 μF. The total charge Q = C_eq * V = (12/13) * 12 = 16 μC. Since the charge is the same across all capacitors in series, the charge on C2 is 16 μC.

Question 14

FIGURE 24-10 -Fig. 24-10 shows three capacitors connected to a battery of voltage V = 6 V. The charges on the capacitors are known to be Q = 24 μC for C₁ and C₂, and Q₃ = 96 μC for C₃. What are the values of the capacitances C₁, C₂, and C₃?

Accepted Answer

The answer of FIGURE 24-10 
-Fig. 24-10 shows three capacitors...

Question 15

Two concentric conducting spheres of radii a = 5 cm and b = 10 cm have a potential difference V = 100 V between them. What is the charge carried by each sphere?

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Question 16

A metal cylinder of radius 2.0 mm is concentric with another metal cylinder of radius 5.0 mm. If the space between the cylinders is filled with air and the length of the cylinders is 50 cm, the capacitance of the arrangement is

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Question 17

A parallel-plate capacitor has plates of area 0.80 m² separated by a distance of 3.0 mm. What is this capacitor's capacitance?

Accepted Answer

The capacitance of a parallel-plate capacitor is given by the formula C = ε₀(A/d), where ε₀ is the permittivity of free space (8.85 × 10⁻¹² F/m), A is the area of the plates, and d is the separation between the plates. Substituting the given values, C = (8.85 × 10⁻¹² F/m)(0.80 m²)/(3.0 × 10⁻³ m) = 2.4 × 10⁻⁹ F.

Question 18

A 5.0 μF and a 7.0 μF capacitor are connected in series across an 8.0-V DC source. What is the voltage across the 5.0 μF capacitor?

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The answer of A 5.0 μF and a 7.0 μF...

Question 19

A 12 mF capacitor is connected in series with a 4 mF capacitor, the combination being connected across a 6 V power supply. The charge on the 12 mF capacitor is

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The answer of A 12 mF capacitor is connected in...

Question 20

FIGURE 24-7 
-What is the equivalent capacitance of the capacitor network shown in Fig. 24-7? (All the capacitors have a capacitance C = 5 μF. The voltage of the battery is V = 6V.)

Accepted Answer

The answer of FIGURE 24-7 
-What is the equivalent capacitance...

Quiz 24: Capacitance, Dielectrics, Electric Energy Storage

A parallel-plate capacitor has a voltage V = 6.0 V between its plates. Each plate carries a surface charge density σ = 7.0 nC/m2. What is the separation of the plates?

The capacitance per unit length of a coaxial cable, made of two concentric cylinders, is 50 pF/m. What is the radius of the outer cylinder if the radius of the inner one is 1.0 mm?

A parallel plate capacitor with plate separation of 4.0 cm has a plate area of 4.0 × 10-2 m2. What is the capacitance of this capacitor with air between these plates?

The magnitude of the charge on each plate of a parallel plate capacitor is 4 μC and the potential difference between the plates is 80 V. What is the capacitance of this capacitor?

FIGURE 24-8 -A system of capacitors is connected across a 90 V DC voltage source as shown in Fig. 24-8. What is the equivalent capacitance of this system?