A parallel plate capacitor was made with two rectangular plates, each with a length of $l = 3\ \text{cm}$ and breadth of $b = 1\ \text{cm}$. The distance between the plates is $3\ \mu\text{m}$. Out of the following, which are the ways to increase the capacitance by a factor of 10?
A. $l = 30\ \text{cm}$, $b = 1\ \text{cm}$, $d = 1\ \mu\text{m}$
B. $l = 3\ \text{cm}$, $b = 1\ \text{cm}$, $d = 30\ \mu\text{m}$
C. $l = 6\ \text{cm}$, $b = 5\ \text{cm}$, $d = 3\ \mu\text{m}$
D. $l = 1\ \text{cm}$, $b = 1\ \text{cm}$, $d = 10\ \mu\text{m}$
E. $l = 5\ \text{cm}$, $b = 2\ \text{cm}$, $d = 1\ \mu\text{m}$
Choose the correct answer from the options given below:
Answer: (D) C and E only
$C = \dfrac{\epsilon_0 lb}{d} \propto \dfrac{lb}{d}$. Originally $\dfrac{lb}{d} = \dfrac{3\times1}{3} = 1$ (cm²/μm); we need 10.
- A: $\dfrac{30\times1}{1} = 30$
- B: $\dfrac{3\times1}{30} = 0.1$
- C: $\dfrac{6\times5}{3} = 10$ ✓
- D: $\dfrac{1\times1}{10} = 0.1$
- E: $\dfrac{5\times2}{1} = 10$ ✓
C and E only.
Solution by Sreeraj P, M.Sc Physics