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Current Question (ID: 17038)

Question:

$\text{A series combination of inductance } (L) \text{ and resistance } (R) \text{ is connected to a battery of emf } E. \text{ The final value of current depends on:}$

Options:

1. $L \text{ and } R$
2. $E \text{ and } R$
3. $E \text{ and } L$
4. $E, L, \text{ and } R$

Solution:

$\text{Initially, the induced emf (or back emf) is there due to the growth of current through the circuit.}$ $\text{The inductance behaves as an open-circuit. Once the current up to its final value } I_0, \text{ there occurs no more change in the current.}$ $\text{The back emf induced in the inductance reduces to zero. It behaves like a short-circuit.}$ $\text{Hence the final value of the current is } I_0 = \frac{E}{R}, \text{ which depends only on } E \text{ and } R.$

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
}