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Alternating Current question

2022 · 28 Jul · Shift 2 · Q53
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  5. /2022 · 28 Jul · Shift 2 · Q53

Alternating Current question

2022 · 28 Jul · Shift 2 · Q53

JEE MainPhysicsAlternating CurrentMCQ+4 / −1
A transformer operating at primary voltage 8 kV8 \,\mathrm{kV}8kV and secondary voltage 160 V160 \mathrm{~V}160 V serves a load of 80 kW80 \mathrm{~kW}80 kW. Assuming the transformer to be ideal with purely resistive load and working on unity power factor, the loads in the primary and secondary circuit would be
  1. A
    800 Ω800 \,\Omega800Ω and 1.06 Ω1.06 \,\Omega1.06Ω
  2. B
    10 Ω10 \,\Omega10Ω and 500 Ω500 \,\Omega500Ω
  3. C
    800 Ω800 \,\Omega800Ω and 0.32 Ω0.32 \,\Omega0.32Ω
  4. D
    1.06 Ω1.06 \,\Omega1.06Ω and 500 Ω500 \,\Omega500Ω
View written solutionFree

Correct answer: C

  1. Given data
  • Primary voltage: Vp=8 kV=8000 VV_p = 8\,\text{kV} = 8000\,\text{V}Vp​=8kV=8000V
  • Secondary voltage: Vs=160 VV_s = 160\,\text{V}Vs​=160V
  • Load power: P=80 kW=80000 WP = 80\,\text{kW} = 80000\,\text{W}P=80kW=80000W
  • Transformer is ideal and load is purely resistive, so power factor =1=1=1

For an ideal transformer, Pp=Ps=80000 WP_p = P_s = 80000\,\text{W}Pp​=Ps​=80000W


  1. Find primary-side load resistance

Since the load is resistive, P=V2RP = \frac{V^2}{R}P=RV2​ So, Rp=Vp2P=(8000)280000R_p = \frac{V_p^2}{P} = \frac{(8000)^2}{80000}Rp​=PVp2​​=80000(8000)2​ Rp=64×1068×104=800 ΩR_p = \frac{64\times 10^6}{8\times 10^4} = 800\,\OmegaRp​=8×10464×106​=800Ω


  1. Find secondary-side load resistance

Similarly, Rs=Vs2P=(160)280000R_s = \frac{V_s^2}{P} = \frac{(160)^2}{80000}Rs​=PVs2​​=80000(160)2​ Rs=2560080000=0.32 ΩR_s = \frac{25600}{80000} = 0.32\,\OmegaRs​=8000025600​=0.32Ω


  1. Match with options

Primary and secondary loads are: 800 Ωand0.32 Ω800\,\Omega \quad \text{and} \quad 0.32\,\Omega800Ωand0.32Ω

This matches Option C.


  1. Comparison with stored answer

Stored correct answer: C

Our derived answer: C

So, the derived answer agrees with the stored correct answer.

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