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.
FigureA B

Answer 1

Answer:

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:

Ceq = [(1×3)/(1+3)+(2×62)+6]

= 3/4+12/8

= 9/4 μF

= 2.25 µF

∴ Ceq = 2.25 µF

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

And,

Ceq = 2.25 µF

Answer 2

Explanation:

• 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:

          Ceq=1×31+3+2×62+6=34+128=94 μF=2.25 µF∴ Ceq = 2.25 µF

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

          Ceq = 2.25 µF