What Is the Equivalent Capacitance of Capacitors in Series and Parallel?

[v0id19]

Quick capacitor question

Homework Statement

Three capacitors are connected to a battery as shown in the figure below. Their capacitances are C1 = 3C, C2 = C, and C3 = 5C

What is the equivalent capacitance of this set of capacitors (in terms of C)?

Homework Equations

In parallel, C_tot=C₁+C₂+...+C_n
In series, 1/C_tot=1/C₁+1/C₂+...+1/C_n

The Attempt at a Solution

my book never says how to add capacitors that are both in series and parallel, so i have no idea. i know the formulas above, but idk how to combine them...

 

[Dadface]

Do it in two parts.Use your first equation above -this gives you the single capacitor that can replace C2 and C3 and now you are left with this single capacitor in series with C1

 

[thomate1]

As a scientist, it is important to have a strong understanding of basic principles and equations in order to approach new problems. In this case, we can use a combination of the parallel and series equations to determine the equivalent capacitance of the set of capacitors.

First, we can see that C1 and C2 are connected in parallel, so we can use the equation Ctot = C1 + C2 to find the equivalent capacitance of these two capacitors. This gives us Ctot = 3C + C = 4C.

Next, we can see that C3 is connected in series with the combination of C1 and C2, so we can use the equation 1/Ctot = 1/C1 + 1/C2 + 1/C3 to find the total inverse capacitance. Substituting in the values from before, we get 1/Ctot = 1/4C + 1/5C, which simplifies to 9/20C.

Finally, we can take the inverse of this value to find the equivalent capacitance: Ctot = 20/9C.

In summary, the equivalent capacitance of this set of capacitors is 20/9 times the value of one of the individual capacitors (C). This approach can be used for any combination of capacitors in a circuit, as long as we understand the principles of parallel and series connections.