[Electricity & Magnetism] Finding the voltage of a battery.

[24karatbear]

Homework Statement

Hello. I just need someone to check if I'm approaching the problem correctly (the steps I've taken are given below).

I drew a quick sketch of the circuit here: http://i.imgur.com/mClttXn.png?1

In the problem, I am given the capacitances of A, B, and C. I am also given the voltage across capacitor B. My goal is to find the voltage of the battery.

Homework Equations

Equivalent capacitance (series) = (cap1*cap2)/(cap2+cap1)
Equivalent capacitance (parallel) = cap1 + cap2 + ... + capn
Voltage = Q/C
Total voltage (series) = V1 + V2
Charge = CV

The Attempt at a Solution

Here are the steps I would take to find the voltage of the battery:

I first find the equivalent capacitance across A and B, the two caps in parallel. Since capacitors in parallel have equal voltages, the voltage across the combined capacitor is the same as the one across capacitor B (let's pretend it was 9V. So the voltage across the combined cap is 9V).

Now, I have the combined cap in series with capacitor C. Since the voltage across the battery is the sum of the voltages of the combined cap and cap C (please correct me if I'm wrong here), I need to find the voltage across C. To do this, I'll need the charge on C. Since the two caps are in series, I can find the charge Q of cap C by finding the charge Q on the combined cap (since the two charges should be equal). Once I find Q, I just divide that by the capacitance of C to obtain the voltage across C.

The voltage of the battery = voltage across combined cap + voltage across C.

Am I doing this correctly?

 

[gneill]

Your method looks okay.

 

[24karatbear]

Your method looks okay.

Thank you!

 

[Linghunt]

Yep you are on track, you only made it much harder than it is. Think of the caps as Impedance loads (Z), Just happen to be capacitance this time.

you got Series and || down for them.

Think to use a Voltage diver... Xc is 1/wc and Xl is wL and Xr is just R

If you think Impedance be easier if one of the Caps is a R or an L. I think Z ...

 

[HalfLostAndSearching]

Hello, it looks like you have a good understanding of the concepts involved in finding the voltage of a battery in a circuit with capacitors. Your approach seems correct, but there are a few things to consider.

Firstly, when you find the equivalent capacitance of A and B in parallel, make sure to use the formula for parallel capacitors (Ceq = C1 + C2). The formula you have listed is for capacitors in series.

Secondly, when you say "Since capacitors in parallel have equal voltages, the voltage across the combined capacitor is the same as the one across capacitor B," this is not always true. In this specific problem, the voltage across the combined capacitor will be the same as the voltage across capacitor B, but this is not always the case. In general, when capacitors are in parallel, the voltage across each capacitor will be the same, but the total voltage across the parallel combination may be different.

Finally, when you find the charge on the combined capacitor, make sure to use the formula Q = CV, where V is the voltage across the combined capacitor, not just the voltage across capacitor B.

Overall, your approach seems correct, but just make sure to use the correct formulas and consider the specific conditions of the problem. Keep up the good work!