What is the equivalent capacitance of three capacitors?

Open in App

Solution

Step 1. Assumption:
Let there be three capacitors of capacitance $C_{a}$ , $C_{b}$ and $C_{c}$ respectively. Let $C$ be the equivalent capacitance of the three capacitors.
Step 2. Diagram for parallel connection:
Step 3. The calculation for parallel series:
The expression for $C$ , the equivalent capacitance is,
$\begin{array}{rcl} \frac{1}{C} & = & \frac{1}{C_{a}} + \frac{1}{C_{b}} + \frac{1}{C_{c}} \\ \frac{1}{C} & = & \frac{C_{b} C_{c} + C_{a} C_{c} + C_{a} C_{b}}{C_{a} + C_{b} + C_{c}} \\ C & = & \frac{C_{a} + C_{b} + C_{c}}{C_{b} C_{c} + C_{a} C_{c} + C_{a} C_{b}} \end{array}$
Step 4. Diagram for series connection:

Step 5. The calculation for series connection:
The expression for $C$ , the equivalent capacitance is,
$C = C_{a} + C_{b} + C_{c}$

Suggest Corrections

Similar questions

Q. What is the equivalent capacitance of the system of capacitors between

A & B

Q. 87.The capacitances of. Three capacitors are in the ratio of 1:2:3 the difference in the equivalent capacitance for their series and parallel combination .is 6 mue F . what are the capacitance of the capacitors?

The equivalent capacitance of three capacitors of capacitance $C_{1}, C_{2}$ and $C_{3}$ connected in parallel is 12 units and the product $C_{1} C_{2} C_{3} = 48$ . When the capacitors $C_{1}$ and $C_{2}$ are connected in parallel the equivalent capacitance is 6 units. Then the capacitance are :

Q. Three identical capacitors, each of capacitance

C

, are wired as shown above
When both switches are closed, the equivalent capacitance is:

Q. Find the equivalent capacitance of three capacitors of capacitance

3 μ F

10 μ F

and

15 μ F

connected in (1) series (2) parallel.

Join BYJU'S Learning Program