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Current Question (ID: 16737)

Question:

$\text{The resistances of the four arms } P, Q, R \text{ and } S \text{ in a Wheatstone's bridge are } 10 \, \Omega, 30 \, \Omega, 30 \, \Omega \text{ and } 90 \, \Omega \text{ respectively.}$ $\text{The emf and internal resistance of the cell are } 7 \, \text{V} \text{ and } 5 \, \Omega \text{ respectively.}$ $\text{If the galvanometer resistance is } 50 \, \Omega \text{ the current drawn from the cell will be:}$

Options:

1. $0.2 \, \text{A}$
2. $0.1 \, \text{A}$
3. $2.0 \, \text{A}$
4. $1.0 \, \text{A}$

Solution:

$\text{Hint: } I = \frac{E}{R + r}$ $\text{Step: Find the current drawn from the cell.}$ $\text{For a balanced Wheatstone's bridge;} \frac{P}{Q} = \frac{R}{S}$ $\text{so terminals of the galvanometer will be at the same potential no current will flow through it.}$ $\text{The net resistance of the circuit is given by;} R_{\text{net}} = \frac{40 \times 120}{40 + 120} = 30 \, \Omega$ $\text{The current drawn from the cell is given by;} I = \frac{E}{R + r}$ $\text{Substitute the known values we get;} \Rightarrow I = \frac{7}{30 + 5} = 0.2 \, \text{A}$ $\text{Hence, option (1) is the correct answer.}$

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Upload a JSON file containing LaTeX/MathJax formatted question, options, and solution.

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
}