Q. 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 $3\,\mu$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, $d=1\,\mu$m B. $l=3$ cm, $b=1$ cm, $d=30\,\mu$m C. $l=6$ cm, $b=5$ cm, $d=3\,\mu$m D. $l=1$ cm, $b=1$ cm, $d=10\,\mu$m E. $l=5$ cm, $b=2$ cm, $d=1\,\mu$m Choose the correct answer from the options given below:
A) A only
B) C only
C) B and D only
D) C and E only
Explanation
[Solution by Dr. Abubacker] $C\propto\frac{lb}d$. Original: $\frac{3\cdot1}3=1$. A: $\frac{30}1=30$; B: $\frac3{30}=0.1$; C: $\frac{6\cdot5}3=10$; D: $\frac1{10}=0.1$; E: $\frac{5\cdot2}1=10$. So only C and E give a factor of 10. Answer (4).
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.