The capacitance of a capacitor, C, is inversely proportional to

1. Analyze the question

The question asks for the physical factor that is inversely proportional to the capacitance ($C$) of a parallel-plate capacitor.

2. Explain the concept

To understand this, we look at the standard formula for the capacitance of a parallel-plate capacitor:

Where:

• $C$ = Capacitance
• $\varepsilon_0$ = Permittivity of free space
• $\varepsilon_r$ = Relative permittivity (dielectric constant)
• $A$ = Area of the plates
• $d$ = Distance between the plates

From this formula, we can see the relationships:

• $C$ is directly proportional to the area ($A$).
• $C$ is directly proportional to the dielectric constant ($\varepsilon_r$).
• $C$ is inversely proportional to the distance between the plates ($d$).

3. Show the solution

• Option A (Area): Since $C \propto A$, this is a direct relationship.
• Option B (Dielectric substance): Since $C \propto \varepsilon_r$, this is a direct relationship.
• Option C (Distance between plates): Since $C = \frac{k}{d}$ (where $k$ is a constant), $C$ is inversely proportional to $d$. As the distance between the plates increases, the capacitance decreases.
• Option D (Direction of the plate): This is irrelevant to the formula for capacitance.

4. Identify the answer

The correct option is C.

5. Exam Tip

Think of a capacitor like a sandwich. If you pull the two slices of bread (the plates) further apart (increase $d$), the "attraction" or electric field between them weakens, which reduces the capacitance. Remember: "Area up, C up; Distance up, C down."