Import Question JSON

Current Question (ID: 16859)

Question:

$\text{In an ammeter, } 0.2\% \text{ of the main current passes through the galvanometer. If the resistance of the galvanometer is } G, \text{ the resistance of the ammeter will be:}$

Options:

1. $\frac{1}{499}G$
2. $\frac{499}{500}G$
3. $\frac{1}{500}G$
4. $\frac{500}{499}G$

Solution:

$\text{The galvanometer is converted to ammeter by applying small resistance parallel to the galvanometer known as shunt.}$ $\text{Potential drop across galvanometer } = I_g \times R_g$ $\text{Potential drop across shunt } = I_s \times R_s$ $\text{As they are parallel, the potential drop remains the same}$ $\text{Let initial current } = I$ $\text{Current passing through galvanometer } = I \times 0.2\% = I \times 0.2/100$ $\text{Current passing through shunt } = I \times 99.8\% = I \times 99.8/100$ $I_g \times R_g = I_s \times R_s$ $0.002R_g = 0.998R_s$ $R_s = \frac{G}{499}$ $\text{Resistance of ammeter } = \frac{R_s R_g}{R_s + R_g}$ $= \frac{G}{500}$

Import JSON File

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
}