Current Density

Step 1: Apply Kirchhoff's Current Law (KCL).

Kirchhoff's Current Law states that the total current flowing into a junction must equal the total current flowing out of the junction. Mathematically:

$%5Ctext%7BTotal%20current%20in%7D%20%3D%20%5Ctext%7BTotal%20current%20out%7D.$

Step 2: Identify the currents.

Currents flowing towards the junction: $0.5%20%5C%2C%20%5Ctext%7BmA%7D$ and $5%20%5C%2C%20%5Ctext%7BmA%7D$ .
Currents flowing away from the junction: $1%20%5C%2C%20%5Ctext%7BmA%7D$ , $x%20%5C%2C%20%5Ctext%7BmA%7D$ , and $2%20%5C%2C%20%5Ctext%7BmA%7D$ .

Step 3: Set up the equation using KCL.

The total current flowing into the junction is:

$0.5%20%2B%205%20%3D%205.5%20%5C%2C%20%5Ctext%7BmA%7D.$

The total current flowing out of the junction is:

$1%20%2B%20x%20%2B%202%20%3D%20x%20%2B%203%20%5C%2C%20%5Ctext%7BmA%7D.$

Equating the total currents:

$5.5%20%3D%20x%20%2B%203.$

Step 4: Solve for $x$ .

Rearrange the equation to isolate $x$ :

$x%20%3D%205.5%20-%203%20%3D%202.5%20%5C%2C%20%5Ctext%7BmA%7D.$

Final Answer: The value of $x$ is $%5Cmathbf%7B2.5%20%5C%2C%20%5Ctext%7BmA%7D%7D$ , which corresponds to option $%5Cmathbf%7B(2)%7D$ .

High-Yield Trend

Chapter Questions
1 MCQs

Official Solution

Current Density

High-Yield Trend

Chapter Questions 1 MCQs

Official Solution

Chapter Questions
1 MCQs