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Voltage and current for a circuit with two elements in series are experssed as follows : ν(t) = 170 sin (6280 t + π/3) Volts i(t) = 8.5 sin (6280 t + π/2) Amps (i) Plot the two waveforms. (ii) Determine the frequency in Hz. (iii) Determine the power factor stating its nature. (iv) What are the values of the elements ? |
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Answer» (i) Two sinusoidal wave forms with a phase-difference of 30° (= π/2 − π/3) are to be drawn. Each waveform completes a cycle in 1 milli-second, since f = 1000 Hz. The waveform for current leads that for the voltage by 30°. At ωt = 0, the current is at its positive peak, while the voltage will be at its positive peak for ωt = π/6 = 30°. Peak value are 170 volts and 8.5 amp. (ii) ω = 6280 radiation/sec, f = ω/2π = 1000 Hz (iii) RMS value of voltage = 170/√2 = 120 volts RMS value of current = 8.5/√2 = 6 amp. Impedance = V/I = 120/6 = 20 ohms Power factor = cos 30°, Leading = 0.866, Since the current leads the voltage, the two elements must be R and C. R = Z cos φ = 20 × 0.866 = 17.32 ohms Xc = Z sinφ = 20 × 0.50 = 10ohms C = 1/(ωXc) = (1000 x 1000)/(6280 x 10) = 15.92mF |
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