# Finding charge on a capacitor given potential difference across two points

• member 731016
In summary, for part (b) of the problem, the solution involves finding the voltage across the upper equivalent capacitor and using it to calculate the charge stored by C3. The charge on the upper group of capacitors is equal to the total charge, and the same charge is on the lower group, since they are in series. The notation for the upper equivalent capacitors is labeled as Q total.
member 731016
Homework Statement
Relevant Equations
For this part(b) of this problem,

The solution is

However, I tried solving (b) like this:

Since ##Q_{total} = 363 \times 10^{-6} C## then ##Q_1 = 181.5 \times 10^{-6} C ## since the equivalent upper capacitor is in series with the equivalent bottom capacitor so should store the same amount of charge.

Since ##C_{upper} = 8.67 \times 10^{-6} C## then voltage across upper equivalent capacitor is ##\frac {181.5}{8.67} = 21V ## then charged stored by ##C_3## is ##Q_3 = 2 \times 10^{6} \times 21 = 4.2 \times 10^{-5} ##

I don't understand why they use the total charge for the upper capacitors when they only store half the charge.
Many thanks!

What do you label as Q1?

member 731016
nasu said:
What do you label as Q1?

I'm not sure, just some notation for the upper equivalent capacitors charge.

Then this is already labeled as Q total. This is the charge on the upper group of capacitors. And the same charge is on the lower group, which is in series with the upper group.
.

member 731016
nasu said:
Then this is already labeled as Q total. This is the charge on the upper group of capacitors. And the same charge is on the lower group, which is in series with the upper group.
.
Thank you for your reply @nasu! I forgot capacitor in series have the same charge!

## What is the formula to find the charge on a capacitor given the potential difference across two points?

The formula to find the charge (Q) on a capacitor is Q = C * V, where C is the capacitance of the capacitor in farads (F), and V is the potential difference across the capacitor in volts (V).

## How do you determine the capacitance of a capacitor?

The capacitance of a capacitor can be determined using the formula C = ε₀ * (A/d) for a parallel plate capacitor, where ε₀ is the permittivity of free space, A is the area of one of the plates, and d is the distance between the plates. For other types of capacitors, the capacitance may be given by the manufacturer or determined experimentally.

## What units are used for charge, capacitance, and potential difference?

The charge (Q) is measured in coulombs (C), the capacitance (C) is measured in farads (F), and the potential difference (V) is measured in volts (V).

## Can the charge on a capacitor be negative?

The charge on a capacitor can be considered negative if the reference point is taken such that the potential difference is negative. However, in practice, we usually refer to the magnitude of the charge, which is always positive. The sign indicates the direction of the electric field.

## What happens to the charge on a capacitor if the potential difference is doubled?

If the potential difference (V) across a capacitor is doubled, the charge (Q) on the capacitor will also double, assuming the capacitance (C) remains constant. This is because the charge is directly proportional to the potential difference (Q = C * V).

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