Arrange the following capacitor configurations in increasing order of their capacitances:
(A) A parallel plate capacitor with air medium between the plates, each of area 10 cm2 and separation between plates 5 mm
(B) A parallel plate capacitor with plate area 20 cm2 and separation between plates 4 mm
(C) A spherical capacitor of diameter 10 cm.
(D) A parallel plate capacitor with plate area 8 cm2 and separation between plates 5 mm and a dielectric material (\( \varepsilon_r = 2 \)) in between the plates
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → (A), (D), (B), (C)
A parallel plate capacitor has \( C = \varepsilon_r \varepsilon_0 A/d \), and an isolated spherical conductor of radius R has \( C = 4\pi\varepsilon_0 R \). Writing every capacitance as a multiple of \( \varepsilon_0 \) (in metres) makes the comparison direct. (B) has no dielectric mentioned, so it is taken as air, \( \varepsilon_r = 1 \).
(A) air medium, plate area 10 cm2, separation 5 mm — \( \displaystyle C_A = \frac{\varepsilon_0 \times 10\times10^{-4}\,\mathrm{m^{2}}}{5\times10^{-3}\,\mathrm{m}} = 0.20\,\varepsilon_0 \)
(B) plate area 20 cm2, separation 4 mm — \( \displaystyle C_B = \frac{\varepsilon_0 \times 20\times10^{-4}\,\mathrm{m^{2}}}{4\times10^{-3}\,\mathrm{m}} = 0.50\,\varepsilon_0 \)
(C) spherical capacitor of diameter 10 cm — \( \displaystyle C_C = 4\pi\varepsilon_0 \times 0.05\,\mathrm{m} \approx 0.63\,\varepsilon_0 \)
(D) plate area 8 cm2, separation 5 mm, dielectric \( \varepsilon_r = 2 \) — \( \displaystyle C_D = \frac{2\,\varepsilon_0 \times 8\times10^{-4}\,\mathrm{m^{2}}}{5\times10^{-3}\,\mathrm{m}} = 0.32\,\varepsilon_0 \)
So \( C_A \lt C_D \lt C_B \lt C_C \), that is, (A), (D), (B), (C).