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Current Electricity question

2025 · 3 Apr · Shift 2 · Q59
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Current Electricity question

2025 · 3 Apr · Shift 2 · Q59

JEE MainPhysicsCurrent ElectricityMCQ+4 / −1
A motor operating on 100 V draws a current of 1 A . If the efficiency of the motor is 91.6%91.6 \%91.6%, then the loss of power in units of cal/s\mathrm{cal} / \mathrm{s}cal/s is
  1. A
    6.2
  2. B
    2
  3. C
    8.4
  4. D
    4
View written solutionFree

Correct answer: B

  1. Input electrical power

The motor operates at V=100 V,I=1 AV = 100\ \text{V}, \qquad I = 1\ \text{A}V=100 V,I=1 A

So the input power is Pin=VI=100×1=100 WP_{\text{in}} = VI = 100 \times 1 = 100\ \text{W}Pin​=VI=100×1=100 W

  1. Efficiency relation

Efficiency is η=PoutPin=91.6%=0.916\eta = \frac{P_{\text{out}}}{P_{\text{in}}} = 91.6\% = 0.916η=Pin​Pout​​=91.6%=0.916

Hence output power is Pout=0.916×100=91.6 WP_{\text{out}} = 0.916 \times 100 = 91.6\ \text{W}Pout​=0.916×100=91.6 W

  1. Power loss

Loss of power is Ploss=Pin−Pout=100−91.6=8.4 WP_{\text{loss}} = P_{\text{in}} - P_{\text{out}} = 100 - 91.6 = 8.4\ \text{W}Ploss​=Pin​−Pout​=100−91.6=8.4 W

Since 1 W=1 J/s1\ \text{W} = 1\ \text{J/s}1 W=1 J/s we have Ploss=8.4 J/sP_{\text{loss}} = 8.4\ \text{J/s}Ploss​=8.4 J/s

  1. Convert into cal/s

Using 1 cal≈4.2 J1\ \text{cal} \approx 4.2\ \text{J}1 cal≈4.2 J

Therefore, Ploss=8.44.2=2 cal/sP_{\text{loss}} = \frac{8.4}{4.2} = 2\ \text{cal/s}Ploss​=4.28.4​=2 cal/s

  1. Check options
  • A: 6.26.26.2 ❌
  • B: 222 ✅
  • C: 8.48.48.4 ❌ (this is in W or J/s, not cal/s)
  • D: 444 ❌

Therefore, the correct answer is Option B.

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