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Alternating Current question

2024 · 30 Jan · Shift 2 · Q82
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Alternating Current question

2024 · 30 Jan · Shift 2 · Q82

JEE MainPhysicsAlternating CurrentNumerical+4 / −1
A power transmission line feeds input power at 2.3 kV2.3 \mathrm{~kV}2.3 kV to a step down transformer with its primary winding having 3000 turns. The output power is delivered at 230 V230 \mathrm{~V}230 V by the transformer. The current in the primary of the transformer is 5 A5 \mathrm{~A}5 A and its efficiency is 90%90 \%90%. The winding of transformer is made of copper. The output current of transformer is ‾A\underline{\hspace{2cm}}A​A.
Numerical answer
View written solutionFree

Correct answer: 45

  1. Given data
  • Primary voltage: Vp=2.3 kV=2300 VV_p = 2.3\,\text{kV} = 2300\,\text{V}Vp​=2.3kV=2300V
  • Secondary voltage: Vs=230 VV_s = 230\,\text{V}Vs​=230V
  • Primary current: Ip=5 AI_p = 5\,\text{A}Ip​=5A
  • Efficiency of transformer: η=90%=0.9\eta = 90\% = 0.9η=90%=0.9

We need the output current IsI_sIs​.


  1. Input power to transformer

The electrical input power is

Pin=VpIp=2300×5=11500 WP_{\text{in}} = V_p I_p = 2300 \times 5 = 11500\,\text{W}Pin​=Vp​Ip​=2300×5=11500W


  1. Output power using efficiency

Efficiency is defined as

η=PoutPin\eta = \frac{P_{\text{out}}}{P_{\text{in}}}η=Pin​Pout​​

So,

Pout=ηPin=0.9×11500=10350 WP_{\text{out}} = \eta P_{\text{in}} = 0.9 \times 11500 = 10350\,\text{W}Pout​=ηPin​=0.9×11500=10350W


  1. Find secondary current

Output power is also

Pout=VsIsP_{\text{out}} = V_s I_sPout​=Vs​Is​

Thus,

Is=PoutVs=10350230=45 AI_s = \frac{P_{\text{out}}}{V_s} = \frac{10350}{230} = 45\,\text{A}Is​=Vs​Pout​​=23010350​=45A


  1. Final answer

45\boxed{45}45​

The given number of primary turns and the copper winding information are not needed for this calculation.

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