001 (part 1 of 3) 10.0 points An oscillating emf drives a series com- bination o

Question

001 (part 1 of 3) 10.0 points An oscillating emf drives a series com- bination of a resistor and an air-gap ca- pacitor with cireular plates, with emf of (150 V)sin(500 radians/s), resistance of 0.6 MS2, radius of 44 cm, and separation of 1.2 m, as shown below 0.6 M1 44 cm ircular plate capacitor (150 V) sin (500 radians/s)t] Find the rms current Ims in the resis- tor. The speed of light is 2.99792 x 108 m/s, the permeability of free space is 4× 10 T m/A, and the permittivity of free space is 8.85419 x 10-12 C2/N. m2 Answer in units of mA 002 (part 2 of 3) 10.0 points Find the rms value of the displacement cur rent between the capacitor plates Answer in units of mA 003 (part 3 of 3) 10.0 points Find the rms value of the induced magnetic field strength between the capacitor plates at a distance of 30 cm from the center of the plates. Answer in units of T

Explanation / Answer

C = e0 A / d

C = (8.854 x 10^-12) (pi 0.44^2) / (1.2 x 10^-3)

C = 4.49 x 10^-9 F

w = 500 rad/s

Xc = 1 / w C = 0.445 x 10^6 ohm = 0.445 Mohm

Z = sqrt[ XC^2 + R^2] = 0.747 M ohm

Irms= Vrms / Z = (150/ 0.747)/sqrt(2)

= 0.142 x 10^-3 A Or 0.142 mA  

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Id_rms = 0.142 mA
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B ( 2 pi r) = u0 Id

B (2 x pi x 0.30) = (4pi x 10^-7) (0.142 x 10^-3)

B = 9.46 x 10^-11 T

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