An oscillating emf drives a series combination of a resistor and an air-gap capa

Question

An oscillating emf drives a series combination of a resistor and an air-gap capacitor with circular plates, with emf of (170 V)sin[(500 radians/s) t], resistance of 0.9 Mohm, radius of 30 cm, and separation of 1.2 mm, as shown below. (170 V) sin[(500 radians/s) t) Find the rms current I_rms in the resistor. The speed of light is 2.99792 times 10^8 m/s, the permeability of free space is 4pi times 10^-7 T. m/A, and the permittivity of free space is 8.85419 times 10^-12 C^2/N. m^2. Answer in units of mA.

Explanation / Answer

Capacitance, C = e0 A / d

       = (8.85419 x 10^-12 x pi x 0.30^2) / (1.2 x 10^-3)

     = 2.086 x 10^-9 F

rectance of capacitor , Xc = 1 / wC = 1 / (500 x 2.086 x 10^-9 ) = 0.96 x 10^6 ohm = 0.96 M ohm

R = 0.9 M ohm

Impedance = sqrt(R^2 + Xc^2) = 1.32 M ohm  

Irms = ( Emax / Z ) / sqrt(2)   = ((170)/(1.32 x 10^6)) / (sqrt(2))

Irms = 9.135 x 10^-5 A = 0.091 mA

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