The instantaneous values of two alternating voltages are represented respectively by v1 = 60 sinθ volts and v2 = 40 sin(θ − π/3) volts. Derive an expression for the instantaneous

The instantaneous values of two alternating voltages are represented respectively by v1 = 60 sinθ volts and v2 = 40 sin(θ − π/3) volts. Derive an expression for the instantaneous value of: (a) the sum; (b) the difference of these voltages. (a) It is usual to draw the phasors in the position corresponding to θ = 0,* i.e. OA in Fig. 9.20 is drawn to scale along the x-axis to represent 60 V, and OB is drawn π/3 radians or 60° behind OA to represent 40 V. The diagonal OC of the parallelogram drawn on OA and OB represents the phasor sum of OA and OB. By measurement, OC = 87 V and angle φ between OC and the x-axis is 23.5°, namely 0.41 rad; hence: Instantaneous sum of the two voltages = 87 sin(θ − 23.5°) V Alternatively, this expression can be found thus: Horizontal component of OA = 60 V

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