Question

Convince yourself that parts (a), (b) and (c) figure (31-E13) are identical. Find the capacitance between the points A and B of the assembly.

Answer 1

Parts (a), (b) and (c) are identical, as all of them form a bridge circuit. In that circuit, capacitors of 1 µF and 2 µF are connected to terminal A and the 5 µF capacitor and capacitors of 3 µF and 6 µF are connected to terminal B and the 5 µF capacitor.

For the given situation, it can be observed that the bridge is in balance; thus, no current will flow through the 5 µF capacitor.
So to simplify the circuit, 5 µF capacitor can be removed from the circuit.
Now, 1 µF and 3 µF capacitors are in series.
And 2 µF and 6 µF capacitors are also in series combination.
These two combination are in parallel with each other.
The equivalent capacitance can be calculated as:

$$\begin{gathered} C_{\mathrm{eq}}=\frac{1\times 3}{1+3}+\frac{2\times 6}{2+6} \\ =\frac{3}{4}+\frac{12}{8}=\frac{9}{4}\mathrm{\mu F}=2.25\mu F \end{gathered}$$
∴ C_eq = 2.25 µF

Thus, parts (a), (b) and (c) are identical.

And,

C_eq = 2.25 µF