Question

What is the meaning of electrical capacity of a conductor? Find the unit of the electrical capacity of the conductor.

Hint:

Remember that the capacitance of a conductor depends on its geometry and the surrounding material. For conductors with large surface area and small separation, capacitance is higher.

Answer 1

The electrical capacity, or capacitance, of a conductor refers to its ability to store electric charge when a potential difference is applied across it. The capacitance \(C\) of a conductor is defined as the amount of charge \(Q\) it can store per unit potential difference \(V\). Mathematically, it is given by the equation:
\[ C = \frac{Q}{V} \] Where:
- \(C\) is the capacitance in farads (F),
- \(Q\) is the charge stored on the conductor in coulombs (C),
- \(V\) is the potential difference across the conductor in volts (V).
The unit of capacitance is the farad (F), which is defined as the amount of charge that can be stored per unit potential difference. In terms of SI units, we can express the farad as:
\[ 1~\text{F} = 1~\frac{\text{C}}{\text{V}} \] This means that if a conductor has a capacitance of 1 farad, it will store 1 coulomb of charge when a potential difference of 1 volt is applied across it.
The electrical capacity (or capacitance) depends on the physical characteristics of the conductor, such as its surface area, shape, and the dielectric properties of the material surrounding it. For a parallel plate capacitor, for example, the capacitance is given by:
\[ C = \epsilon_0 \frac{A}{d} \] Where:
- \(C\) is the capacitance,
- \(\epsilon_0\) is the permittivity of free space (\(8.85 \times 10^{-12}~\text{F/m}\)),
- \(A\) is the area of the plates,
- \(d\) is the distance between the plates.
Thus, the electrical capacity of a conductor is the ratio of the charge stored to the potential difference, and its unit is the farad (F).