  Question

Figure 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 0.15A.(a) Calculate the capacitance and the rate of change of potential difference between the plates.(b)Obtain the displacement current across the plates.(c)IsKirchhoffs first rule (junction rule) valid at each plate ofthe capacitor Explain. Solution

(a)$$C\, =\, \varepsilon _0A/d=\, 80.1\, pF$$$$\displaystyle \frac{dQ}{dt}\, =\, C\, \displaystyle \frac{dV}{dt}$$$$\displaystyle \frac{dV}{dt}\, =\, \displaystyle \frac{0.15}{80.1\, \times\, 10^{-12}}\, =\, 1.87\, \times\, 10^9\, V\, s^{-1}$$ (b) The displacement current across the plate is same as the conduction current. Hence, the displacement current , $$I_d=0.15\ A$$ (c) Yes, Kirchhoff's first rule is valid at each plate of the capacitor provided that we take the sum of conduction and displacement for the current.PhysicsNCERTStandard XII

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