A potential difference V(t) = V0sin ωt ismaintained across a parallel-plate capacitor withcapacitance C consisting of two circular parallel plates. Athin wire with resistance R connects the centers of the twoplates, allowing charge to leak between plates while theyare charging.(a) Obtain expressions for the leakage current Ires(t) in thethin wire. Use these results to obtain an expression for thecurrent Ireal(t) in the wires connected to the capacitor.(b) Find the displacement current in the space between theplates from the changing electric field between the plates.(c) Compare Ireal(t) with the sum of the displacementChapter 16 | Electromagnetic Waves 733current Id(t) and resistor current Ires(t) between theplates, and explain why the relationship you observe wouldbe expected.

Delmar's Standard Textbook Of Electricity
7th Edition
ISBN:9781337900348
Author:Stephen L. Herman
Publisher:Stephen L. Herman
Chapter20: Capacitance In Ac Circuits
Section: Chapter Questions
Problem 5PP: Three capacitors having capacitance values of 20F,40F, and 50F are connected in parallel to a 60 -...
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A potential difference V(t) = V0
sin ωt is
maintained across a parallel-plate capacitor with
capacitance C consisting of two circular parallel plates. A
thin wire with resistance R connects the centers of the two
plates, allowing charge to leak between plates while they
are charging.
(a) Obtain expressions for the leakage current Ires(t) in the
thin wire. Use these results to obtain an expression for the
current I
real(t) in the wires connected to the capacitor.
(b) Find the displacement current in the space between the
plates from the changing electric field between the plates.
(c) Compare I
real(t) with the sum of the displacement
Chapter 16 | Electromagnetic Waves 733
current Id
(t) and resistor current Ires(t) between the
plates, and explain why the relationship you observe would
be expected.

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