Calculating charge on a capacitor in a DC circuit

In summary, to calculate the charge on the capacitor in this circuit, you need to find the potential difference across the capacitor terminals. At steady state, the capacitor acts as an open circuit and can be removed from the circuit. By analyzing the circuit without the capacitor, you can find the potential at the capacitor terminals and use it to calculate the charge on the capacitor using Q = CV.
  • #1
dancavallaro
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0

Homework Statement


See attached image for a circuit diagram. The assumptions are that transients have died out and the currents and charges have reached their equilibrium values. I have to calculate the charge on the capacitor.

Homework Equations


[tex]Q_C = C \Delta V[/tex]
[tex]V_C(t) = Q(t)/C = V_0(1-e^{-t/RC})[/tex]

The Attempt at a Solution


I honestly am not really sure where to start with this. Given the formula above, it's clear that I need to calculate the voltage across the capacitor. But I only know how to calculate the voltage across something with a known resistance, using Ohm's Law. I guess my first question would be, how can I calculate the voltage across a capacitor? And once I have that, I can just use [tex]Q_C = C \Delta V[/tex] to calculate the charge.

edit: nevermind, I figured this out on my own.
 

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  • #2
The idea is to find the potential difference across the capacitor. From that the charge on it can be found.

At steady state there will be no current flowing to or from the capacitor; it is effectively an open circuit. So remove the capacitor from the circuit and determine the potential across the points where it was connected. This is easily done if we find them with respect to the reference node.

On the left we have a potential divider comprising a 10 V battery and two equal resistors. So the potential at their junction will be half the battery voltage, or 5 V. On the right side there is a battery in series with a resistor. Since there's no current flowing ("open" capacitor), there's no potential change across the resistor. So the potential at that capacitor terminal is equal to that battery voltage, or 3 V.

The capacitor "sees" the difference between those potentials, or 2 V. So the charge on the capacitor is, given by Q = CV, is

##Q = (0.01~μF)(2~V) = 20~nC##
 

1. How do you calculate the charge on a capacitor in a DC circuit?

The charge on a capacitor in a DC circuit can be calculated using the formula Q = CV, where Q is the charge in coulombs, C is the capacitance in farads, and V is the voltage across the capacitor in volts.

2. What is the unit of measurement for charge on a capacitor?

The unit of measurement for charge on a capacitor is coulombs (C).

3. Can you calculate the charge on a capacitor if the capacitance and voltage are unknown?

No, both the capacitance and voltage are necessary to calculate the charge on a capacitor in a DC circuit.

4. Is the charge on a capacitor constant in a DC circuit?

Yes, the charge on a capacitor remains constant in a DC circuit unless the voltage or capacitance changes.

5. How does the charge on a capacitor affect the overall energy storage in a circuit?

The charge on a capacitor is directly proportional to the amount of energy stored in the capacitor. Therefore, increasing the charge on a capacitor will increase the overall energy storage in the circuit.

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