An oscillating emf drives a series combination
of a resistor and an air-gap capacitor
with circular plates, with emf of
(280 V) sin[(600 radians/s)t] , resistance of
1 MΩ , radius of 31 cm , and separation of
1 mm , as shown below.
1 MΩ
31 cm
circular
plate capacitor
1 mm
(280 V) sin[(600 radians/s)t]
Find the rms current Irms in the resistor.
The speed of light is 2.99792 × 108 m/s,
the permeability of free space is 4π ×
10−7 T · m/A, and the permittivity of free
space is 8.85419 × 10−12 C
2
/N · m2
.
Answer in units of mA

Question

An oscillating emf drives a series combination
of a resistor and an air-gap capacitor
with circular plates, with emf of
(280 V) sin[(600 radians/s)t] , resistance of
1 MΩ , radius of 31 cm , and separation of
1 mm , as shown below.
1 MΩ
31 cm
circular
plate capacitor
1 mm
(280 V) sin[(600 radians/s)t]
Find the rms current Irms in the resistor.
The speed of light is 2.99792 × 108 m/s,
the permeability of free space is 4π ×
10−7 T · m/A, and the permittivity of free
space is 8.85419 × 10−12 C
2
/N · m2
.
Answer in units of mA

anonymous · Answer

attachment

radar · Answer

Determine the capacitance value, it is determined solely by the physical characteristics given.
(determine area of plates, the distance of separation is given and the dielectric is air......be careful with the mm vs cm dimensions).
Next determine the frequency in Hz from the 600 radians per second.
Now determine the reactance of the capacitor.
and determine the impedance of the series arrangement of the capacitor and resistance for the calculated frequency.
determine the RMS current by converting the voltage to RMS value and dividing by the impedance.  This sounds involved, and may be even more involved than I show.