Capacitance of a Conductor

Think of a conductor like a water tank and potential like water level. A wider tank (larger capacitance) needs more water (charge) to raise its level by the same amount — capacitance is a measure of "storage capacity" for charge, just as tank width measures storage capacity for water.

Capacitance is the ability of a conductor to store electric charge.

When charge q is given to an isolated conductor, its potential V rises. Experimentally, q is directly proportional to V:

where C is a constant called the capacitance of the conductor.

C = \[\frac {q}{V}\]

Capacitance is the charge required to raise the potential of a conductor by one unit (1 volt).

q–V Graph:

• The graph of charge (q) vs potential (V) for a conductor is a straight line through the origin.
• The slope of the line equals the capacitance (C) of the conductor.

Given: q = 8 μC, V = 200 V

Step 1: Write the formula: C = q/V
Step 2: Substitute values: C = \[\frac {8×10^{−6}}{200}\]
Step 3: Simplify: C = 4 × 10⁻⁸ F
Step 4: Convert to standard practical unit: C = 40 nF

Answer: C = 40 nF