How Do You Solve Capacitor Series Circuit Problems?

[ulfric]

Good day everyone. Please help with these questions.

The circuit is a series of 3 capacitors with a battery.
C1 = C
C2 = 2C
C3 = 3C

How do you find the voltage across the first capacitor in a series of 3?

How do you find the charge Q on the first capacitor?

How do you find the equivalent capacitance Ceq for this combination of capacitors in series?

I had these questions on a test and know the answers but not how to arrive at them. I am usually quick on the uptake but teaching this basic stuff adequately is apparently beneath my professor and the text is terrible! (stay away from Young & Geller!)

Thanks for any help you can provide.

 

[SGT]

The equivalent capacitance of a series of n capacitors is done by the expression:
$$\frac{1}{C_{eq}}=\sum_{k=1}^n \frac{1}{C_k}$$
The charge in all capacitors is the same.
Charge, voltage and capacitance are related by:
$$q = CV$$

 

[kyle8921]

Hello there,

First of all, it's great that you are seeking help and trying to understand these concepts better. I can assure you that learning the fundamentals is crucial for success in any scientific field.

To answer your questions, let's start with the basics. In a series circuit, the voltage across each component is the same. This means that the voltage across the first capacitor (C1) will be the same as the voltage across the second (C2) and third (C3) capacitors. So, to find the voltage across C1, you can simply measure the voltage across any of the capacitors in the series circuit.

Next, to find the charge (Q) on the first capacitor, we can use the formula Q = CV, where C is the capacitance and V is the voltage. Since we know the capacitance of C1 (C), we can simply multiply it by the voltage across C1 to find the charge on it.

Finally, to find the equivalent capacitance (Ceq) for the series combination of capacitors, we can use the formula 1/Ceq = 1/C1 + 1/C2 + 1/C3. In this case, since all the capacitors have different values, we need to first find the reciprocal of each capacitance (1/C1, 1/C2, 1/C3), add them together, and then take the reciprocal of the sum to get the equivalent capacitance.

I hope this helps. If you have any further questions, don't hesitate to ask. Remember, it's important to fully understand the basics before moving on to more complex concepts. Good luck with your studies!