Chapter 25

In the figure V = 9.8 V, C1 = C2 = 24 μF, and C3 = C4 = 15 μF. What is the charge on capacitor 4?

**** need answer

Which is true about the Ceq for series capacitors?

Ceq is less than the least capacitance in the series. To demonstrate this answer, pick some easy numbers for two capacitors in series and plug them into the equation for series capacitors.

Use the slider to decrease the distance d between the plates to the smallest possible value allowed by the simulation. Observe the effect on the voltmeter reading. How has the capacitance changed as a result of this operation?

Decreased d means increased C

If we decrease the plate area of a parallel-plate capacitor, what happens to the capacitance—that is, the charge per volt?

Decreases Think about the space to store the charge—with less plate area, the capacity to store charge is less.

How has the magnitude of the electric field between the plates |E→| been affected by this operation?

E new = E old

Here are four circuits, each with two capacitors and a battery. Which of the circuits have a parallel combination of capacitors?

In each circuit the battery applies the same potential difference across the pair of plates. The capacitors have one of their plates directly connected and have their other plates directly connected.

If we decrease the separation between the plates, what happens to the capacitance—that is, the charge per volt?

Increases With a smaller gap, the positive and negative charges are now closer.

Every expression for a capacitance involves ɛ0 and a length measure. Let L represent that length. The capacitance depends on what power of L?

L

This figure shows a combination of capacitors across which a potential difference of V = 12.5 V is applied by a battery. Are capacitors 1 and 3 in series?

No They are certainly connected one after the other, but when the applied potential shifts charge from the top plate of capacitor 3, that charge is not constrained to move to only the bottom plate of capacitor 1. There is another route: to the bottom plate of capacitor 2. For the same reason, capacitors 2 and 3 are not series.

To get back closer to capacitor 1, we need to undo the simplification step that replaced capacitors 1 and 2 with their equivalent capacitor 12. Which rule was involved in that replacement?

Par-V

Our last simplification step was to replace the connection of capacitor 12 and capacitor 3 with its equivalent capacitor 123. Which rule was involved in that replacement?

Seri-q

Four capacitors re connected to make the circuit shown below. A. Identify any capacitors that are in series in this network. B. Identify any capacitors that are in parallel in this network.

Top plates of C3 and C4 are connected together with no other connections to them, but the bottom plates are not. C3 and C4 must have q3 = q4, so they are in series. Top plates of C1 and C2 are connected together and the bottom plates are connected together. C1 and C2 must have V1 = V2, so they are in parallel.

How does the potential difference V across the battery compare with the sum of these potential differences?

V = V1 + V2 + V3

When we replace capacitors 1 and 2 with their equivalent C12, we have the following circuit. Is capacitor 12 in series with capacitor 3?

Yes Again apply the test for series capacitances: When the potential is applied, the charge that shifts from the top plate of capacitor 3 must entirely go to the bottom plate of capacitor 12 (there is no other route for it to take).

This figure shows a combination of capacitors across which a potential difference of V = 12.5 V is applied by a battery. Are capacitors 1 and 2 in parallel?

Yes Their top plates are directly connected by wire and so are their bottom plates. The potential difference across capacitor 1 is the same as across capacitor 2.

Here is a circuit with four capacitors and a battery. (a) In the figure, are capacitors 1 and 2 in series? (b) Are capacitors 2 and 3 in series?

a) No. There is a connection between the capacitors but there is also a side branch. That breaks the requirement for series capacitors. b) Yes. There is only one direct route between the capacitors.

How has the charge q been affected by this operation? You may assume that the voltmeter measured the potential difference between the plates without affecting the charge distribution on either plate.

q new = q old You already know from question 3 that Cnew=10Cold. The simulation shows how the potential difference changes, ΔVnew=ΔVold/10. The relationship q=CΔV then tells us that q does not change. This is in agreement with the hint that was provided. We are told that the voltmeter cannot change the charge distribution on either plate. As the plates are moved closer together, there is no place for the charge on either plate to go, so q must remain the same.