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3. The electric field of an electromagnetic wave is described by the equation 4. A 300 92 resistor R and a 200 JF capacitor are connected in series across an ac power supply which has a voltage Vin and oscillates at an angular frequency w. By (x, t) = 6 sin [0.5xx(3 + ot)] where t is in seconds and x is in meters. a) Determine the wavelength, frequency, and velocity of the wave. (5 pts) b) Determine the direction of vibration and direction of propagation of the electric field? (5 pts) c) Write an equation of the magnetic field (5 pts) d) Determine the direction of vibration and direction of propagation of the magnetic field? (5 pts) Solution a) Determine that the ratio of the output voltage, Voutput, across the capacitor to the input voltage Vinput from the source as a function of the angular frequency @. (5 pts) b) What value does this ratio approach as the frequency tends to zero? (2.5 pts) as the frequency tends to infinity? (2.5 pts) c) Plot a graph of the Voutput Vinout as a function of the angular frequency w. (5 pts) d) At what frequency, f, is the ratio equal to 0.5 when R = 300 9 and C = 200 HE? (5 pts) Solution