The document calculates the instantaneous value of a wave resulting from combining a 50 Hz fundamental wave with a third harmonic wave at 0.005 seconds. The fundamental wave has a maximum value (Emax) of 339 V. The third harmonic wave has a Emax of 113 V. It finds that the fundamental wave equals 339 V at 0.005 seconds, while the third harmonic equals -113 V. It then sums these values to determine that the instantaneous voltage of the combined wave at 0.005 seconds is 226 V.

1. Example 1 Determine the instantaneous value of the resultant wave at 0.005 seconds when the third harmonic is added to a 50 Hz fundamental if the two waves have the following values. Fundamental: - Emax = 339 V Third harmonic - Emax = 113 V. e = E 1m sin ω t + E 3m sin 3 ω t . Value of fundamental e = E 1m sin ω t = 339 x sin (2 x π x 50 x 0.005 x 57.29579) = 339 x sin 90  = 339 x 1 e = 339 V Value of third harmonic e = E 3m sin 3 ω t = 113 x sin (2 x π x 150 x 0.005 x 57.29579) = 113 x sin 270  = 113 x (-1) e = - 113 V Instantaneous voltage at 0.005 seconds = E 1m sin ω t + E 3m sin 3 ω t. = 339 + (-113) e = 226 V

2. Third harmonics Example 1 Determine the instantaneous value of the resultant wave at 0.005 seconds when the third harmonic is added to a 50 Hz fundamental if the two waves have the following values. Fundamental: - Emax = 339 V Third harmonic - Emax = 113 V. e = E 1m sin ω t + E 3m sin 3 ω t .