Q160 / 160 · TS EAMCET 2018 (07 May Shift 1) · Physics
For a television network, $5 \times 10^5$ channels are granted. If the central frequency of the microwave link is $25 \mathrm{GHz}$ and the alloted bandwidth for each channel is $2 \mathrm{kHz}$, then how much percentage of the link is used for the network?
- Correct answerA$4 \%$
- B$10 \%$
- C$25 \%$
- D$5 \%$
Solution
Let $x \%$ of link is used for network.
Given, central frequency $=25 \mathrm{GHz}$
$=25 \times 10^9 \mathrm{~Hz}$
Bandwidth of channels $=x \%$ of $25 \mathrm{GHz}$
$=\frac{x}{100} \times 25 \times 10^9=25 x \times 10^7$
Number of channel
$\begin{aligned}<br />& =\frac{\text { Total Bandwidth }}{\text { Bandwidth needed per channel }} \\<br />5 \times 10^5 & =\frac{25 \times \times 10^7}{2 \times 10^3} \\<br />10 \times 10^8 & =25 \times \times 10^7 \\<br />25 x & =100 \\<br />\Rightarrow \quad x & =4 \%<br />\end{aligned}$
Given, central frequency $=25 \mathrm{GHz}$
$=25 \times 10^9 \mathrm{~Hz}$
Bandwidth of channels $=x \%$ of $25 \mathrm{GHz}$
$=\frac{x}{100} \times 25 \times 10^9=25 x \times 10^7$
Number of channel
$\begin{aligned}<br />& =\frac{\text { Total Bandwidth }}{\text { Bandwidth needed per channel }} \\<br />5 \times 10^5 & =\frac{25 \times \times 10^7}{2 \times 10^3} \\<br />10 \times 10^8 & =25 \times \times 10^7 \\<br />25 x & =100 \\<br />\Rightarrow \quad x & =4 \%<br />\end{aligned}$
Hence, the correct answer is option: 'A'.