The dielectric constant of an insulator  in a transmission line is 2.25. Calculate velocity factor of the transmission line

Answer

To solve the problem of calculating the velocity factor of a transmission line with a dielectric constant of 2.25, we can follow these steps:

### Step 1: Understand the Formula for Velocity Factor
The velocity factor (VF) of a transmission line is given by the formula:
\[ VF = \frac{1}{\sqrt{k}} \]
where \( k \) is the dielectric constant of the insulator.

### Step 2: Identify the Dielectric Constant
From the problem, we know that the dielectric constant \( k \) is 2.25.

### Step 3: Substitute the Dielectric Constant into the Formula
Now, we substitute the value of \( k \) into the velocity factor formula:
\[ VF = \frac{1}{\sqrt{2.25}} \]

### Step 4: Calculate the Square Root
Next, we calculate the square root of 2.25:
\[ \sqrt{2.25} = 1.5 \]

### Step 5: Calculate the Velocity Factor
Now, we can find the velocity factor by substituting the square root back into the formula:
\[ VF = \frac{1}{1.5} \]
Calculating this gives:
\[ VF = 0.6667 \]

### Step 6: Round the Result
Finally, we can round the result to two decimal places:
\[ VF \approx 0.67 \]

### Final Answer
The velocity factor of the transmission line is approximately **0.67**.

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