Question

Question #da0e2

Answer 1

`T_1^@C->"Initial temp of the shunt winding"`

`T_2^@C->" Temp of the winding after a full load run"`

`R_1->"Resistance of winding at "T_1=20^@C`

`R_2->"Resistance of winding at "T_2`

`alpha->"Temp. coeff. of Resistance"=0.0043Omega"/"^@C`

`"At "T_1" Voltage"(V)=400V`
`"and current through " R_1 " is "I_1=2.25A`

`"At "T_2" Voltage"(V)=400V`
`"and current through " R_2 " is "I_2=2A`

`"So " R_1=V/I_1=400/2.25=1600/9Omega`

`and R_2=V/I_2=400/2=200Omega`

Now

`R_2=R_1(1+alphaxx(T_2-T_1))`

`=>(T_2-T_1)alpha=(R_2-R_1)/R_1`

`=>T_2-T_1=(R_2-R_1)/(R_1alpha)`

`=>T_2-T_1=(9/1600)(200-1600/9)/(0.0043)`

`=>T_2-T_1=1/(8xx0.0043)~~25.84^@C`

So average rise in temperature
`~~25.84^@C`