Import Question JSON

Current Question (ID: 16613)

Question:

$\text{A current passes through a wire of variable cross-section in steady-state as shown. Then incorrect statement is:}$

Options:

1. $\text{Current density increases in the direction of the current.}$
2. $\text{Potential increases in the direction of the current.}$
3. $\text{Electric field increases in the direction of the current.}$
4. $\text{Drift speed increases in the direction of the current.}$

Solution:

$\text{Hint: The current density is directly proportional to the electric field.}$ $\text{Step 1: Find the variation of the current density and the electric field.}$ $\text{The current density is given by, } \left| \vec{j} \right| = \frac{i}{A}. $ $\text{So, as the cross-section area decreases in the direction of the current, the current density increases in the direction of the current.}$ $\text{As the current density and the electric field are proportional to each other, the electric field also increases in the direction of the current.}$ $\text{Step 2: Find the variation of potential and the drift velocity.}$ $\text{Since the electric field is increasing, the drift speed also increases in the direction of the current.}$ $\text{The potential decreases in the direction of the electric current.}$

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
}