Question

A telephonic communication service is working at carrier frequency of $10GHz$. Only $10\%$ of it is utilized for transmission. How?

• A. $2\times {10}^5$
• B. $2\times {10}^6$
• C. $2\times {10}^3$
• D. $2\times {10}^4$

Answer 1

The correct option is A

$2\times {10}^5$

The explanation for the correct answer is,

Step 1. Given Data:

Carrier frequency $$\begin{gathered} =10GHz \\ =10\times {10}^{9}Hz \end{gathered}$$

Step 2. $10\%$ is used in transmission:

$\frac{10}{100}\times 10\times {10}^{9}Hz=1\times {10}^{9}Hz$

Step 3. As we know:

Each channel requires, $5\times {10}^{3}Hz$

No of channels, $n$ = (carrier frequency$x0.1$) $/$ channel bandwidth

$$\begin{gathered} \Rightarrow n=\frac{(0.1x10x{10}^9)}{(5x{10}^3)} \\ \therefore n=2x{10}^5 \end{gathered}$$

Hence, the correct option is (A).