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Figure 8.01 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» Solution :(a) It is given that radius of each circular plate R = 12CM = 0.12 m, separation between the plates d = 5.0 mm `=5.0xx10^(-3)m` and charging current `I=0.15A` `therefore"Capacitance of the capacitor C"=(epsilon_(0).A)/(d)=(epsilon_(0)piR^(2))/(d)=(8.85xx10^(-12)xx3.14xx(0.12)^(2))/(5.0xx10^(-3))` `=80.1xx10^(-12)F=80.1pF` and rate of change of POTENTIAL difference between the plates of capacitor `(dV)/(dt)=(d)/(dt)((d)/(C ))=(1)/(C ).(dq)/(dt)=(I)/(C )["As "(dq)/(dt)=I]` `therefore""(dV)/(dt)=(0.15)/(80.1xx10^(-12))=1.87xx10^(9)VS^(-1)`. (B) Displacement current `I_(d)=epsilon_(0).(dphi_(E))/(dt)=epsilon_(0).(d)/(dt)(EA)=epsilon_(0).A(dE)/(dt)` But we known that `E=(sigma)/(epsilon_(0))=(q)/(epsilon_(0)A),"hence,"(dE)/(dt)=(1)/(epsilon_(0)A).(dq)/(dt)=(1)/(epsilon_(0)A).I` `therefore"Displacement current "I_(d)=epsilon_(0)A.(1)/(epsilon_(0)A)I=I` (c) Yes, Kirchhoff.s first rule is valid at each plate of the capacitor provided that we take current as the sum of conduction current and displacement current. With this understanding at fist plate of capacitor the incoming current `I_(d)=` outgoing current I. |
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