A parallel plate capacitor was made with two rectangular plates, each with a length of l=3 cm and breath of b=1 cm. The distance between the plates is 3 μ m. Out of the following, which are the ways to increase the capacitance by a factor of 10 ?
A. l=30 cm, b=1 cm, d=1 μ m
B. l=3 cm, b=1 cm, d=30 μ m
C. l=6 cm, b=5 cm, d=3 μ m
D. l=1 cm, b=1 cm, d=10 μ m
E. l=5 cm, b=2 cm, d=1 μ m
Choose the correct answer from the options given below:

Solution

Physics sir · 3 steps

Capacitance goes as area over gap, so just check which sets make lb/d ten times bigger.

1. What C depends on. For a parallel plate capacitor C = (ε₀ l b)/d. So C is proportional to lb/d, and you only need to compare that ratio.
2. Original value. Keep l and b in cm and d in μm, since the units cancel in the comparison. At the start, lb/d = (3 × 1)/3 = 1. A tenfold increase needs lb/d = 10.

   Set	lb (cm²)	d (μm)	lb/d	Change in C
   A	30 × 1 = 30	1	30	30 times
   B	3 × 1 = 3	30	0.1	1/10 of the original
   C	6 × 5 = 30	3	10	10 times
   D	1 × 1 = 1	10	0.1	1/10 of the original
   E	5 × 2 = 10	1	10	10 times

3. So. Only C and E raise the capacitance by a factor of exactly 10, which is option (d).

The idea to keep. When only the plate size and gap change, compare area/d against the original. Bigger area helps, smaller gap helps, and both effects multiply.

Answer from the NTA final answer key. Solution by PrepWiser.