Question

Figure 8.6 shows a capacitor made of two circular plates each ofradius 12 cm, and separated by 5.0 cm. The capacitor is beingcharged by an external source (not shown in the figure). Thecharging current is constant and equal to 0.15A. (a) Calculate the capacitance and the rate of change of potentialdifference between the plates. (b) Obtain the displacement current across the plates. (c) Is Kirchhoff’s first rule (junction rule) valid at each plate of thecapacitor? Explain.

Answer 1

Given: the radius of each plate is 12 cm, distance between each plate is 5.0 cm. and the charging current is 0.15 A.

a)

The capacitance between two plates is given as,

C= ε 0 A d

Where, A is the area of each plate and d is the distance between each plate.

By substituting the given values in the above expression, we get

C= 8.85× 10 −12 ×π× ( 0.12 ) 2 0.05 =80.1 pF

Charge on each plate is given as,

q=CV

Where, V is the voltage on each plate.

Differentiate both sides with respect to time.

d dt q=C d dt V I=C d dt V d dt V= I C

By substituting the given values in the above expression, we get

d dt V= 0.15 80.1× 10 −12 =1.87× 10 9   Vs −1

Thus, the capacitance is 80.1 pF and the rate of change of potential difference between the plates is 1.87× 10 9   Vs −1 .

b)

The displacement current is same as the conduction current. Hence, the displacement current is 0.15 A.

c)

Yes, Kirchhoff’s junction rule is valid at each plate of the capacitor if current is interpreted as the sum of conduction and displacement currents.