1% of `10^12` Hz of a satellite link was used for telephony . What is the number of channels (or subscribers ) , if the bandwidth of each channel is 8 KHz ?

Options

A. (a)`2.5xx10^(7)`
B. (b)`1.25xx10^(6)`
C. (c)`2.5xx10^(8)`
D. (d)`1.25xx10^(8)`

Answer

To solve the problem, we need to determine the number of channels (or subscribers) that can be accommodated given the total bandwidth available for telephony and the bandwidth required for each channel.

### Step-by-Step Solution:

1. **Identify the Total Bandwidth Available for Telephony:**
The total bandwidth of the satellite link is given as \(10^{12}\) Hz. Since only 1% of this bandwidth is used for telephony, we can calculate the useful bandwidth.
\[ \text{Useful Bandwidth} = \frac{1}{100} \times 10^{12} \text{ Hz} = 10^{10} \text{ Hz} \]

2. **Determine the Bandwidth of Each Channel:**
The bandwidth for each channel is given as 8 kHz. We need to convert this into Hertz for consistency in units.
\[ \text{Bandwidth of each channel} = 8 \text{ kHz} = 8 \times 10^3 \text{ Hz} \]

3. **Calculate the Number of Channels:**
The number of channels can be calculated using the formula:
\[ \text{Number of Channels} = \frac{\text{Useful Bandwidth}}{\text{Bandwidth of each channel}} \]
Plugging in the values we have:
\[ \text{Number of Channels} = \frac{10^{10} \text{ Hz}}{8 \times 10^3 \text{ Hz}} = \frac{10^{10}}{8 \times 10^3} \]

4. **Simplify the Expression:**
We can simplify this further:
\[ \text{Number of Channels} = \frac{10^{10}}{8 \times 10^3} = \frac{10^{10}}{8} \times \frac{1}{10^3} = \frac{10^{10 - 3}}{8} = \frac{10^7}{8} \]

5. **Calculate the Final Value:**
Now, we can perform the division:
\[ \text{Number of Channels} = 1.25 \times 10^6 \]

Thus, the total number of channels (or subscribers) is \(1.25 \times 10^6\).

### Final Answer:
The number of channels (or subscribers) is \(1.25 \times 10^6\).

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