Numerical problem on dielectric strength of capacitor
In this post, we will solve a numerical problem on the dielectric strength and dielectric constant of capacitor, maximum electric field, maximum potential difference, maximum charge, etc.
Numerical problem on dielectric strength & dielectric constant – solved
Question: A parallel-plate capacitor has plates of dimensions 2.0 cm by 3.0 cm separated by a 1.0-mm thickness of paper.
(A) Find its capacitance.
(B) What is the maximum charge that can be placed on the capacitor?
Dielectric constant of paper = K = 3.7
Dielectric strength of paper = 16 x 106 V/m.
Solution:
(A)
K = 3.7
Area =A= 2×3 cm2 = 6 x 10-4 m2
d=1 mm = 10-3 m
ε0 = 8.85 x 10 -12 C2 / Nm2
Capacitance C = K Aε0 / d = 3.7 x 6 x 10-4 x 8.85 x 10 -12 /10-3 F = 20 x 10-12 F = 20 pF
(B) Dielectric strength of paper = 16 x 106 V/m
Hence, maximum electric field = Emax = 16 x 106 V/m
Max Potential difference Vmax = Emax . d = 16 x 106 x 10-3 V = 16 x 103 V
Hence, here the Maximum Charge = Qmax = C Vmax = 20 x 10-12 x 16 x 103 C = 0.32 μC