CBSE Class 12 · 2006 · CapacitanceShort Answer

The given graph shows the variation of charge

q

versus potential difference

V

for two capacitors

C_{1}

and

C_{2}

. The two capacitors have the same plate separation but the plate area of

C_{2}

is double that of

C_{1}

. Which of the lines in the graph corresponds to

C_{1}

and

C_{2}

and why?

Answer: The line with the larger slope corresponds to $C_{2}$ (line A); the smaller-slope line to $C_{1}$ (line B).

Solution

Since

q = C V

, the slope of a

q

V

line equals the capacitance. As

C = \frac{ε _{0} A}{d}

with the same

d

, the capacitor of larger area has the larger capacitance.

C_{2}

has double the area, so it has the larger slope; hence the steeper line (A) is

C_{2}

and the gentler line (B) is

C_{1}

CBSE Class 12 Board · 2006 · Subjective