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Chapter 24: Problem 3

The distance between the plates of a parallel plate capacitor is reduced by half and the area of the plates is doubled. What happens to the capacitance? a) It remains unchanged. b) It doubles. c) It quadruples. d) It is reduced by half.

Short Answer

Expert verified
a) It halves b) It doubles c) It quadruples d) It remains the same Answer: c) It quadruples

Step by step solution

01

Find the initial capacitance #

To calculate the initial capacitance, we will use the formula C_initial = (ε₀ * A_initial) / d_initial. Here, A_initial and d_initial are the initial area and distance between the plates, respectively. Let's denote the initial capacitance as C₀. C₀ = (ε₀ * A_initial) / d_initial
02

Find the new capacitance #

Since we're given that the area is doubled and the distance between the plates is reduced by half, the new area and distance will be A_new = 2 * A_initial and d_new = 0.5 * d_initial. Now we can find the new capacitance using the same formula as before: C_new = (ε₀ * A_new) / d_new
03

Substitute the new values #

Now we need to substitute the new values of area and distance into the equation for the new capacitance: C_new = (ε₀ * (2 * A_initial)) / (0.5 * d_initial)
04

Simplify the equation #

Now we will simplify the equation to observe any changes in the capacitance: C_new = (ε₀ * 2 * A_initial) / (d_initial * 0.5) C_new = 4 * (ε₀ * A_initial) / d_initial
05

Compare the new capacitance to the initial capacitance #

We can now compare the new capacitance C_new to the initial capacitance C₀: C_new = 4 * C₀ As we can see, the new capacitance is four times the initial capacitance. Thus, the correct answer is: c) It quadruples.

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Most popular questions from this chapter

Does it take more work to separate the plates of a charged parallel plate capacitor while it remains connected to the charging battery or after it has been disconnected from the charging battery?

A capacitor with a vacuum between its plates is connected to a battery and then the gap is filled with Mylar. By what percentage is its energy-storing capacity increased?

A parallel plate capacitor consisting of a pair of rectangular plates, each measuring \(1.00 \mathrm{~cm}\) by \(10.0 \mathrm{~cm},\) with a separation between the plates of \(0.100 \mathrm{~mm},\) is charged by a power supply at a potential difference of \(1.00 \cdot 10^{3} \mathrm{~V}\). The power supply is then removed, and without being discharged, the capacitor is placed in a vertical position over a container holding de-ionized water, with the short sides of the plates in contact with the water, as shown in the figure. Using energy considerations, show that the water will rise between the plates. Neglecting other effects, determine the system of equations that can be used to calculate the height to which the water rises between the plates. You do not have to solve the system.

A parallel plate capacitor of capacitance \(C\) is connected to a power supply that maintains a constant potential difference, \(V\). A close-fitting slab of dielectric, with dielectric constant \(\kappa\), is then inserted and fills the previously empty space between the plates. a) What was the energy stored on the capacitor before the insertion of the dielectric? b) What was the energy stored after the insertion of the dielectric? c) Was the dielectric pulled into the space between the plates, or did it have to be pushed in? Explain.

A \(4.00 \cdot 10^{3}-n F\) parallel plate capacitor is connected to a \(12.0-\mathrm{V}\) battery and charged. a) What is the charge \(Q\) on the positive plate of the capacitor? b) What is the electric potential energy stored in the capacitor? The \(4.00 \cdot 10^{3}-\mathrm{nF}\) capacitor is then disconnected from the \(12.0-\mathrm{V}\) battery and used to charge three uncharged capacitors, a \(100 .-n F\) capacitor, a \(200 .-\mathrm{nF}\) capacitor, and a \(300 .-\mathrm{nF}\) capacitor, connected in series. c) After charging, what is the potential difference across each of the four capacitors? d) How much of the electrical energy stored in the \(4.00 \cdot 10^{3}-\mathrm{nF}\) capacitor was transferred to the other three capacitors?
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