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Current Question (ID: 16658)

Question:

$\text{Two cities are } 150 \text{ km apart. The electric power is sent from one city to another city through copper wires. The fall of potential per km is } 8 \text{ volts and the average resistance per km is } 0.5 \text{ ohm. The power loss in the wire is:}$

Options:

1. $19.2 \text{ W}$
2. $19.2 \text{ kW}$
3. $19.2 \text{ J}$
4. $12.2 \text{ kW}$

Solution:

$\text{Hint: } P = \frac{V_{\text{total}}^2}{R_{\text{total}}}$ $\text{Step: Find the power loss in the wire.}$ $\text{The total potential drop } (V_{\text{total}}) \text{ is given by:}$ $\Rightarrow V_{\text{total}} = \text{Potential drop per km} \times \text{Distance in km}$ $\Rightarrow V_{\text{total}} = 8 \text{ V/km} \times 150 \text{ km} = 1200 \text{ V}$ $\text{The total resistance } (R_{\text{total}}) \text{ over the distance is given by:}$ $\Rightarrow R_{\text{total}} = \text{Resistance per km} \times \text{Distance in km}$ $\Rightarrow R_{\text{total}} = 0.5 \Omega/\text{km} \times 150 \text{ km} = 75 \Omega$ $\text{The power loss } (P) \text{ in the wire is given by:}$ $\Rightarrow P = \frac{V_{\text{total}}^2}{R_{\text{total}}}$ $\Rightarrow P = \frac{(1200 \text{ V})^2}{75 \Omega} \Rightarrow P = 19.2 \text{ kW}$ $\text{Hence, option (2) is the correct answer.}$

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Expected JSON Format:

{
  "question": "The mass of carbon present in 0.5 mole of $\\mathrm{K}_4[\\mathrm{Fe(CN)}_6]$ is:",
  "options": [
    {
      "id": 1,
      "text": "1.8 g"
    },
    {
      "id": 2,
      "text": "18 g"
    },
    {
      "id": 3,
      "text": "3.6 g"
    },
    {
      "id": 4,
      "text": "36 g"
    }
  ],
  "solution": "\\begin{align}\n&\\text{Hint: Mole concept}\\\\\n&1 \\text{ mole of } \\mathrm{K}_4[\\mathrm{Fe(CN)}_6] = 6 \\text{ moles of carbon atom}\\\\\n&0.5 \\text{ mole of } \\mathrm{K}_4[\\mathrm{Fe(CN)}_6] = 6 \\times 0.5 \\text{ mol} = 3 \\text{ mol}\\\\\n&1 \\text{ mol of carbon} = 12 \\text{ g}\\\\\n&3 \\text{ mol carbon} = 12 \\times 3 = 36 \\text{ g}\\\\\n&\\text{Hence, 36 g mass of carbon present in 0.5 mole of } \\mathrm{K}_4[\\mathrm{Fe(CN)}_6].\n\\end{align}",
  "correct_answer": 4
}