Capacitors And Capacitance

Capacitive Reactance

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Step 1: Recall the Concept of Displacement Current

Displacement current is given by:

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Where:

= Displacement current

= Permittivity of free space

= Electric flux

= Time

Step 2: Relate to Conduction Current

In a capacitor circuit, the displacement current in the gap is equal in magnitude to the conduction current in the connecting wires. This ensures continuity of current in the circuit.

Step 3: Conclusion

The displacement current flows in the same direction as the conduction current and has the same magnitude.

To determine the equivalent capacitance between terminal A and terminal B in the given circuit, let's analyze the configuration step by step.

Circuit Analysis:

The circuit consists of four capacitors, each with a capacitance of 2 μF, arranged in a diamond shape as follows:

1. Two capacitors are connected in series on the left side.
2. Two capacitors are connected in series on the right side.
3. These two series combinations are then connected in parallel between terminals A and B.

1. Series Combination on the Left Side:
Capacitors: 2 μF and 2 μF in series.
Equivalent capacitance for series:

2. Series Combination on the Right Side:
Capacitors: 2 μF and 2 μF in series.
Equivalent capacitance for series:

3. Parallel Combination of the Two Series Pairs:
The two 1 μF equivalent capacitors are now in parallel.
Equivalent capacitance for parallel:

Final Answer:

The equivalent capacitance between terminal A and terminal B is: