How to Calculate the Charge on Capacitor C5?

In summary: The charge will distribute unevenly between the capacitors because they have different capacities. The voltage across each capacitor is 12 V, so the total charge on each capacitor will be: Q = 6 μF + 1.6 μF + 5.1 μF + 4.2 μF = 18.8 μF
  • #1
kjlchem
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0

Homework Statement



What is Q5, the charge on C5? V of battery = 12 V.

Homework Equations



C=Q/V

The Attempt at a Solution



V1 + V5 + V(2,3) = Vb
V1 + V5 + V4 = Vb

I have three unknowns and 2 equations. :(
 

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  • #2
kjlchem said:

Homework Statement



What is Q5, the charge on C5? V of battery = 12 V.

Homework Equations



C=Q/V

The Attempt at a Solution



V1 + V5 + V(2,3) = Vb
V1 + V5 + V4 = Vb

I have three unknowns and 2 equations. :(
Look for the total equivalent capacitance instead. Then apply your Relevant Equation to find the charge that is pushed onto that capacitance by the voltage V.
 
  • #3
Great! I got that part right.

I'm confused though on how to find Q2. I know that charge adds across a parallel circuit so Q(total) = Q2 + Q4, but I don't know Q4 either.
 
  • #4
kjlchem said:
Great! I got that part right.

I'm confused though on how to find Q2. I know that charge adds across a parallel circuit so Q(total) = Q2 + Q4, but I don't know Q4 either.

Looks like more algebra will be involved :wink:

You now know the total charge Q that will be put onto the equivalent capacitance comprising C2,C3, and C4. You can work out the equivalent capacitance of C2 & C3 alone (perhaps call it C23), then determine how to divide the total charge Q across the parallel C23 and C4.
 
  • #5
Better algebra than calculus. :)

I know that C23 = 1.22F and that Q2 = Q3 = Q23

I don't see how C23 is related to Q2, except for using the relevant equation. Also, I don't think that Q total divides evenly between C23 and C4 because I've already tried that.
 
  • #6
Do you have any capacitance values?
 
  • #7
kjlchem said:
Better algebra than calculus. :)

I know that C23 = 1.22F and that Q2 = Q3 = Q23

I don't see how C23 is related to Q2, except for using the relevant equation. Also, I don't think that Q total divides evenly between C23 and C4 because I've already tried that.

The charge won't divide evenly between the two. You need to determine how the charge distributes between two parallel capacitors (same voltage across both, different capacities).
 
  • #8
Yep! C1 = C5 = 6 μF, C2 = 1.6 μF, C3 = 5.1 μF, and C4 = 4.2 μF. The battery voltage is V = 12 V.

Okay, I think I get it now.
 

1. What is a capacitor and how does it work?

A capacitor is a passive electrical component that stores energy in an electric field. It consists of two conductive plates separated by an insulating material called a dielectric. When a voltage is applied across the plates, an electric field is created, causing one plate to accumulate positive charge and the other to accumulate negative charge. This process is known as charging, and the capacitor can then hold this charge until it is discharged.

2. What is the role of a capacitor in a circuit?

A capacitor can serve several purposes in a circuit, including energy storage, filtering, and timing. As mentioned before, it can store electrical energy, which can be released when needed. It can also be used to filter out unwanted signals or noise from a circuit. Additionally, capacitors can be used in timing circuits to control the rate of charging and discharging.

3. How do you calculate the capacitance of a capacitor?

The capacitance of a capacitor is determined by its physical dimensions, the material of the plates, and the type of dielectric used. It is measured in farads (F) and is calculated using the formula C = εA/d, where ε is the permittivity of the dielectric material, A is the area of the plates, and d is the distance between the plates.

4. How does a capacitor behave in a DC circuit?

In a DC (direct current) circuit, a capacitor behaves as an open circuit, which means it blocks the flow of current. When a voltage is applied, it charges until it reaches its maximum capacitance. After that, the capacitor will no longer allow current to flow through it. However, if the voltage is removed, the capacitor can discharge its stored energy, allowing current to flow again.

5. How does a capacitor behave in an AC circuit?

In an AC (alternating current) circuit, a capacitor behaves differently than in a DC circuit. It can both store and release energy as the voltage and current change direction. As the voltage increases, the capacitor charges, and as the voltage decreases, the capacitor discharges. This process repeats as the AC cycle continues. Capacitors are often used in AC circuits for power factor correction and filtering.

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