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Question -

Figure 8.6 shows a capacitor madeof two circular plates each of radius 12 cm, and separated by 5.0 cm. Thecapacitor is being charged by an external source (not shown in the figure). Thecharging current is constant and equal to 0.15 A.

(a) Calculate the capacitance and therate of charge of potential difference between the plates.

(b) Obtain the displacement currentacross the plates.

(c) Is Kirchhoff’s first rule (junctionrule) valid at each plate of the capacitor? Explain.



Answer -

Radius of each circular plate, r = 12 cm = 0.12 m

Distancebetween the plates, d = 5 cm =0.05 m

Chargingcurrent, I = 0.15 A

Permittivityof free space, = 8.85 × 10−12 C2 N−1 m−2

(a) Capacitance between the two plates isgiven by the relation,

C 

Where,

A =Area of each plate 

Charge on each plate, q = CV

Where,

V =Potential difference across the plates

Differentiationon both sides with respect to time (t)gives:

Therefore, the change inpotential difference between the plates is 1.87 ×109 V/s.

(b) The displacement current across theplates is the same as the conduction current. Hence, the displacement current, id is0.15 A.

(c) Yes

Kirchhoff’sfirst rule is valid at each plate of the capacitor provided that we take thesum of conduction and displacement for current.

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