# Two battery circuit charging one capacitor

• dtecker
In summary, to determine the magnitude of electric charge stored by the capacitor when the switch is closed, you need to remove the capacitor from the circuit and find the potential across its terminals. This potential will be equal to the potential that the surrounding circuit "wants" to impose across the capacitor. Once you have this potential, you can use Q=VC to calculate the charge on the capacitor.
dtecker
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See attached photo for circuit diagram.

The switch S has been open for a long time. Determine the magnitude of the electric charge stored by the capacitor. Use the following data: C = 3.43 mF, ε1 = 11.0 V, ε2 = 31.9 V, R1 = 3.66 Ω, R2 = 5.04 Ω.

I understand how to determine the magnitude of charge with one battery and one capacitor using Q=VC.
Q=.109 C

However, I don't understand how to evaluate with this circuit setup.

Now the switch is closed, and you wait for a long time. How much electric charge does the capacitor store now?

I attempted to simply add the voltage of the two batteries together then used Q=VC but that isn't right because the current wouldn't flow that way from the 11V battery. The 31.9V battery would split its current between the capacitor and the wire to the other battery and resistor.

What approach do I need to take to calculate the charge on the capacitor with the switch closed?

Thanks

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dtecker said:
What approach do I need to take to calculate the charge on the capacitor with the switch closed?

Hi dtecker,

Welcome to Physics Forums!

A general approach for these types of problem is to "remove" the capacitor from the circuit and determine the potential across the terminals where it was connected:

After sufficient time, the current into or out of the capacitor will be zero (steady state reached), so that the potential across the capacitor must be equal to the potential that the surrounding circuit would "like" to impose across it. Find that potential and you can then determine the charge on the capacitor.

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scottdave

## 1. How does charging a capacitor with two batteries in a circuit work?

When two batteries are connected in a circuit, they create a potential difference or voltage between them. This potential difference causes a current to flow in the circuit, which charges the capacitor. The higher the voltage of the batteries, the faster the capacitor will charge.

## 2. What happens if the batteries in a two battery circuit charging a capacitor have different voltages?

If the batteries have different voltages, the capacitor will charge based on the higher voltage. This means that one battery will contribute more to the charging process than the other, and the capacitor will reach its maximum charge faster. However, if the difference in voltage is too high, it can damage the capacitor.

## 3. How can I determine the charge time for a capacitor in a two battery circuit?

The charge time for a capacitor in a two battery circuit can be calculated using the formula: t = (R x C) x ln(V2/V1), where t is the charge time in seconds, R is the resistance in the circuit, C is the capacitance of the capacitor, V2 is the final voltage, and V1 is the initial voltage. This formula assumes that the capacitor is charging from an initial voltage of 0 to a final voltage of V2.

## 4. Is it possible to overcharge a capacitor in a two battery circuit?

Yes, it is possible to overcharge a capacitor in a two battery circuit. This can happen when the voltage of the batteries is too high, or if the capacitor is left charging for too long. Overcharging a capacitor can cause it to fail or even explode, so it is important to monitor the charging process and stop it when the capacitor reaches its maximum charge.

## 5. What factors can affect the charging time of a capacitor in a two battery circuit?

The charging time of a capacitor in a two battery circuit can be affected by several factors, including the capacitance of the capacitor, the voltage of the batteries, the resistance in the circuit, and the initial and final voltage of the capacitor. Additionally, the type and condition of the batteries can also impact the charging time.

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