Solve Battery & Capacitors Network: Find C2,C3 PD & Q3 Charge

In summary, we have a circuit with a battery and several capacitors, some known and some unknown quantities. The capacitors were initially uncharged and the circuit is in a static state. To solve for the unknowns, we use the relation W=1/2 * CV^2 to find the potential difference across C2, which is equal to the potential difference across C3 since they are parallel. We also use the relation Q=C*V to find the charge on C2 and use that to find the charge on C3.
  • #1
ahazen
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I have a circuit consisting of a battery and several capacitors, some quantities are known and some are not. The capacitors were completely uncharged before the battery was attached and we are considering the static situation. (Be sure to keep at least 3 sig. figs. in your answer for all parts of this problem.)

Given:
Q1: 7.9e-6
C1: 7.1e-6
C2: 1.9e-6
Energy stored on C2: W=5.6e-6 J
C2 is parallel to C3

I found:
the potiential distance across C1 is 1.126 V

I need to find:
-Potenital distance across C2
-Potential difference across C3
-The charge of Q3 on C3


Can you please help me? Thank you:)
 
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  • #2
1) You know the relation
W=1/2 * CV^2
You can find V2 because you know C2 and W2

2) Since C2 and C3 are parallel V2=V3 (Pot. diff. across C2 and C3 are same)3) I assumed C1 is in series with C2 || C3. Q1 is known. Since they are in series total charge in C2||C3 is Q1. (In series connected capacitors the amount of charge stored in each capacitor is same). You can find charge in C2 using relation
Q2=C2V2.
From this Q3= Total charge in C2||C3 (ie., Q1) - Q2
 
  • #3
Ok, thank you:)
 

FAQ: Solve Battery & Capacitors Network: Find C2,C3 PD & Q3 Charge

How do I calculate the unknown values in a battery and capacitor network?

To calculate the unknown values in a battery and capacitor network, you will need to use Kirchhoff's laws and the equations for capacitors and batteries. First, use Kirchhoff's laws to create a system of equations for the network. Then, use the equations for capacitors and batteries to solve for the unknown values.

What is Kirchhoff's voltage law and how is it used in solving battery and capacitor networks?

Kirchhoff's voltage law states that the sum of the voltage drops in a closed loop in a circuit is equal to the sum of the voltage sources in that same loop. This law is used to create a system of equations for a battery and capacitor network, which can then be solved to find the unknown values.

What are the equations for calculating the charge on a capacitor and the potential difference across a capacitor?

The equation for calculating the charge on a capacitor is Q = CV, where Q is the charge in coulombs, C is the capacitance in farads, and V is the potential difference in volts. The equation for calculating the potential difference across a capacitor is V = Q/C, where V is the potential difference in volts, Q is the charge in coulombs, and C is the capacitance in farads.

Can I use Ohm's law to solve battery and capacitor networks?

No, Ohm's law (V = IR) cannot be used to solve battery and capacitor networks because capacitors do not follow Ohm's law. Instead, you will need to use the equations for capacitors and batteries, as well as Kirchhoff's laws, to solve for the unknown values.

What are some common mistakes to avoid when solving battery and capacitor networks?

Some common mistakes to avoid when solving battery and capacitor networks include forgetting to account for the polarity of the capacitors, using the wrong units, not including all components in the system of equations, and not properly simplifying the equations before solving for the unknown values. It is important to carefully check your work and double check your calculations to avoid these mistakes.

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