Question

A moving coil ammeter, a hot-wire ammeter and a resistance of 100 Ω are connected in series with a rectifying device across a sinusoidal alternating supply of 200 V. If the device has a resistance of 100 Ω to the current in one direction and 5.00 Ω to current in opposite direction, calculate the readings of the two ammeters.

Answer 1

R.M.S. current in one direction is = 200/(100 + 100) = 1A

Average current in the first i.e. positive half cycle is = 1/1.11 = 0.9 A

Similarly, r.m.s. value in the negative half-cycle is = − 200/(100 + 500) = − 1/3 A

Average value = (−1/3)/1.11 = −0.3 A

Average value over the whole cycle is = (0.9 − 0.3)/2 = 0.3 A

Hence, M/C ammeter reads 0.3 A

Average heating effect during the +ve half cycle = I²_rms × R = I 2 × R = R

Similarly, average heating effect during the −ve half-cycle is = (−1/3)² × R = R/9

Here, R is the resistance of the hot-wire ammeter.

Average heating effect over the whole cycle is = 1/2(R +  R/9) =  5R/9

If I is the direct current which produces the same heating effect, then

I²R = 5R/9

∴ I = 5/3 = 0.745 A

Hence, hot-wire ammeter indicates 0.745 A