Question

A parallel combination of a 1.13-μF capacitor and a 2.89-μF one is connected in series to a 4.33-μF capacitor. This three-capacitor combination is connected to a 16.1-V battery. Find the charge of each capacitor. Note it is a parallel and a series.

Charge of 4.33-μF capacitor: answer in C

Charge of 1.13-μF capacitor:answer in C

Charge of 2.89-μF capacitor:answer in C

Answer 1

Let C₁=1.13 μF, C₂=2.89 μF, C₃=4.33 μF, and V=16.1 V

First, we need to find the equivalent capacitance of the parallel combination of capacitors 1 and 2. Let's call this C₄.

Now we can find the equivalent capacitance of all capacitors together. Let's call this C_eq.

Remember, now, that capacitors in series have the same charge. Therefore:

So, for C₃ and C₄, the charge is:

Remember, next, that capacitors in parallel have the same voltage. Therefore:

Now V₀ is given, therefore, by:

Now that we have our voltage V₀, Q₁ and Q₂ are given by the equations:

If you work through these steps you should have the charge on every capacitor: Q₁ and Q₂ are directly above. Q₃ is the first charge we solved for further up.