The input voltage v(t) and current i(t) of a converter are given by,

v(t) = 300 sin(ωt) V

i(t) = 10 sin(ωt − π/6) + 2 sin(3ωt + π/6) + sin(5ωt + π/2) A

where, ω = 2π × 50 rad/s. The input power factor of the converter is closest to

Question

The input voltage v(t) and current i(t) of a converter are given by,

v(t) = 300 sin(ωt) V

i(t) = 10 sin(ωt − π/6) + 2 sin(3ωt + π/6) + sin(5ωt + π/2) A

where, ω = 2π × 50 rad/s. The input power factor of the converter is closest to

Accepted Answer

0.845. Voltage is purely fundamental, so only the fundamental current (10 A peak, lagging 30 deg) delivers real power. Power factor = (I1_rms/I_total_rms) x cos(30) = (10/sqrt(105)) x 0.866 = 0.845. The stored 0.867 is wrong.

The input voltage v(t) and current i(t) of a converter are given by, v(t) = 300 sin(ωt) V i(t) = 10 sin(ωt − π/6) + 2 sin(3ωt + π/6) + sin(5ωt + π/2) A where, ω = 2π × 50 rad/s. The input power factor of the converter is closest to

Solution

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