Find the equivalent capacitance of the group of capacitors shown in Figure:


Problem solution

Before proceed to solve this problem it's very important remember rules needed for find equivalent capacitances:

Equivalent capacitance equations:


Equivalent capacitance in parallel

The equivalent capacitance of a parallel combination of capacitors is

Equivalent capacitance in series

If two or more capacitors are connected in series, the equivalent capacitance of the series combination is

Problems involving a combination of capacitors can be solved by applying Equations 1 and 2 repeatedly to a circuit diagram, simplifying it as much as possible. This is followed by working backwards to the original diagram, applying C = Q / V, the fact that parallel capacitors have the same voltage drop, and the fact that series capacitors have the same charge.
Now that we have the subject knowledge of how find equivalent capacitances, we can continue with problem solution!

Application of rules to find equivalent capacitances

First, is needed recall all capacitor as C1, C2, ... , C7. to make more easy algebraic manipulation:
Find the equivalent (eq) capacitance between C1 and C2 capacitors (note that they are in parallel configuration, so we need apply the equation [1] )

As before, find the equivalent (eq) capacitance between Ceq1 and C3 capacitors (note that they are in series configuration, so we need apply the equation [2] )

Continue the process, find the equivalent (eq) capacitance between C4, C5 and C6 capacitors (note that they are in parallel configuration, so we need apply the equation [1] )

Now, find the equivalent (eq) capacitance between Ceq3 and C7 capacitors (note that they are in series configuration, so we need apply the equation [2] )

Last step, find the equivalent (eq) capacitance between Ceq2 and Ceq4 capacitors (note that they are in parallel configuration, so we need apply the equation [1] )


Tricks to find equivalent capacitance


Problems like this vary only on one thing - distribution - the key to solve is identify the capacitors distribution type (parallel or series) and then resume the circuit in to his minimal expression.
If you like this post follow us for more physics problem solutions! and remember.. the physics it's so easy!