Question

On what two factors does the capacity of a condenser depend?

Hint:

Remember the formula for the parallel-plate capacitor: \(C = \kappa \epsilon_0 A / d\). This single formula contains all the factors that affect capacitance. To increase capacitance, you can increase the area (\(A\)), increase the dielectric constant (\(\kappa\)), or decrease the distance (\(d\)).

Answer 1

Step 1: Understanding the Concept:
The capacity, or capacitance (\(C\)), of a condenser (an older term for capacitor) is a measure of its ability to store electric charge. It is defined as the ratio of the magnitude of the charge (\(Q\)) on either conductor to the magnitude of the potential difference (\(V\)) between them: \(C = Q/V\). However, the capacitance itself does not depend on \(Q\) or \(V\); it is determined by the physical characteristics of the capacitor.
Step 2: Key Formula or Approach:
To identify the factors, we can look at the formula for the capacitance of a standard parallel-plate capacitor, which illustrates the dependencies clearly:
\[ C = \frac{\kappa \epsilon_0 A}{d} = \frac{\epsilon A}{d} \] where:
- \(C\) is the capacitance.
- \(\kappa\) (or \(\epsilon_r\)) is the dielectric constant of the material between the plates.
- \(\epsilon_0\) is the permittivity of free space (a constant).
- \(\epsilon = \kappa \epsilon_0\) is the permittivity of the dielectric medium.
- \(A\) is the area of overlap of the plates.
- \(d\) is the distance between the plates.
Step 3: Detailed Explanation of Factors:
From the formula, we can identify the key factors:
1. Geometrical Factors: The capacitance depends on the size, shape, and relative positioning of the conductors. For the parallel-plate capacitor, these are:
- Area of the plates (\(A\)): The capacitance is directly proportional to the area of the plates (\(C \propto A\)). A larger area allows more charge to be stored for the same potential difference.
- Distance between the plates (\(d\)): The capacitance is inversely proportional to the distance between the plates (\(C \propto 1/d\)). Bringing the plates closer increases the electric field between them, which allows more charge to be stored for a given voltage.
2. Dielectric Medium:
- Permittivity of the medium (\(\epsilon\)): The capacitance is directly proportional to the permittivity of the dielectric material placed between the conductors (\(C \propto \epsilon\)). A dielectric material with a higher dielectric constant (\(\kappa\)) increases the capacitance because it reduces the effective electric field, allowing more charge to be stored at the same potential difference.
Step 4: Final Answer:
Therefore, the two main factors determining the capacitance of a condenser are its physical geometry (area of plates, distance between them) and the nature of the dielectric medium separating them.