Question

Question 8.1: Figure 8.6 shows a capacitor made of two circular plates each of radius 12 cm, and separated by 5.0 cm. The capacitor is being charged by an external source (not shown in the figure). The charging current is constant and equal to 0.15 A. (a) Calculate the capacitance and the rate of charge of potential difference between the plates. (b) Obtain the displacement current across the plates. (c) Is Kirchhoff’s first rule (junction rule) valid at each plate of the capacitor? Explain.

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Answer 1

Given,
radius of each circular plate , r = 12cm = 0.12m
distance between the plate, d = 5cm = 0.05m
charging current, I = 0.15A
now, capacitance between the two parallel plats is given by $C = \frac{\epsilon_0A}{d}$
where , A= area of each plate = πr²
= π(0.12)² = 0.0144π m²

now, C = (8.85 × 10^-12 × 0.0144π)/0.05
= 8 × 10^-12 F = 8pF
now, charge on each plate, q = CV
C is capacitance e.g., constant
now, difference q = cV with respect to time.
dq/dt = cdV/dt
as you know, dq/dt = i= current
so, dV/dt = i/C
= 0.15/8 × 10^-12 = 1.87 × 10^10 V/s
therefore the change in potential difference between the plates is 1.87 × 10^10 V/s

(b) displacement current across the plates is same as conduction current. hence, displacement current i = 0.15A

(c)yes , kirchoff's rule is valid in each plate of capacitor provided that we take the sum of conduction and displacement current.