A parallel plate capacitor is made with two rectangular plates, each of length l=3 cm and breadth b=1 cm, the distance between the plates being 3 μ m. Out of the following, which are 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…

Question

A parallel plate capacitor is made with two rectangular plates, each of length l=3 cm and breadth b=1 cm, the distance between the plates being 3 μ m. Out of the following, which are 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.

Accepted Answer

(4) C and E only. C=(ε₀ lb)/d, so the required change is in the single combination (lb)/d. Original (working in cm² per μ m): (3×1)/3=1, so a factor of ten means (lb)/d=10. A: (30×1)/1=30. B: (3×1)/(30)=0.1. C: (6×5)/3=10. D: (1×1)/(10)=0.1. E: (5×2)/1=10. Only C and E give the factor 10.

Step-by-step solution

Why the other options are wrong