Question

The 300 turn primary of a transformer has resistance 0.82 Ω and the resistance of its secondary of 1200 turns is 6.2 Ω. Find the voltage across the primary if the power output from the secondary at 1600V is 32 kW. Calculate the power losses in both coils when the transformer efficiency is 80%

Answer 1

Given data:

N_P = 300, N_S = 1200, V_S = 1600 V, R_P = 0.82Ω,
R_S = 6.2Ω, P_S = 32 KW

1) P_S = V_SI_S

`"I"_"S" = "P"_"S"/"V"_"S"`

`= 32000/1600`

I_S = 20 A

2) `"V"_"P"/"V"_"S" = "N"_"P"/"N"_"S"`

`"V"_"P" = 300/1200 xx 1600`

= 400 V

3) η = `"P"_"S"/("V"_"p""I"_"p")`

`= 80/100 = 32000/(400 xx "I"_"p") = 32000/320`

I_p = 100 A

4) Power loss in primary = (I_P)² × R_P

= 100 × 1000 × 0.82

= 0.82 × 1000

= 8.2000 = 8.2 KW

5) Power loss in secondary = (I_S)² × R_S

= 20 × 20 × 6.2

= 400 × 6.2

= 2480 W = 2.48 KW