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in Physics by (64.8k points)

A single-phase energy meter of the induction type is rated 230-V; 10-A, 50- Hz and has a meter constant of 600 rev/kWh when correctly adjusted. If ‘quadrature’ adjustment is slightly disturbed so that the lag is 85º, calculate the percentage error at full-load 0.8 p.f. lag.

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Td depends among other factors, on sin α where α is the angle between the two alternating fluxes. 

∴ Td ∝ sin α 

If the voltage flux-lagging adjustment is disturbed so that the phase angle between the voltage flux and the voltage is less than 90º (instead of being exactly 90º) the error is introduced. 

Now cos φ = 0.8, φ = cos−1 (0.8) = 36º52′ 

∴ α = 85º − 36º52′ = 48º8′ 

where it should be = 90 − 36º52′ = 53º8′

∴ error  = (sin53º8 + sin48º8)/sin53º8 x 100 = 7%

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