Q.Define capacitance. Derive an expression for the capacitance of a parallel-plate capacitor. (1+2) OR A capacitor of capacity 20 μF is charged with potential 10 V. Another capacitor of capacity 60 μF is charged with potential 30 V. They are connected in such a way that their potential is same. Find the common potential and charge of each capacitor after connection. (1+1+1)

Capacitance is defined as C = Q/V; for a parallel-plate capacitor, computing the field and hence the potential difference from the plate charge gives C = ε₀A/d.

Definition: Capacitance of a conductor (or capacitor) is the ratio of the charge $Q$ given to it, to the resulting potential difference $V$ between its plates:

$C = \dfrac{Q}{V}$

It depends only on the geometry of the conductor/capacitor and the medium between the plates, not on $Q$ or $V$ individually.

Derivation for a parallel-plate capacitor: Consider two large parallel plates, each of area $A$, separated by a small distance $d$, with vacuum between them, carrying charges $+Q$ and $-Q$.

The surface charge density on each plate is $\sigma = Q/A$. The uniform electric field between the plates (from two oppositely charged infinite sheets) is: …