A telephonic communication service is working at carrier frequency of 10 GHz. Only 10% of it is utilized for transmission. How many telephonic channels can be transmitted simultaneously if each channel requires a bandwidth of 5 kHz ?

Options

A. `2xx10^(6)`
B. `2xx10^(3)`
C. `2xx10^(4)`
D. `2xx10^(5)`

Answer

To determine how many telephonic channels can be transmitted simultaneously, we need to follow these steps:

### Step 1: Determine the total bandwidth available for transmission.
The carrier frequency is given as 10 GHz, and only 10% of this frequency is utilized for transmission.

\[ \text{Total Bandwidth} = 10\% \text{ of } 10 \text{ GHz} = 0.1 \times 10 \text{ GHz} = 1 \text{ GHz} \]

### Step 2: Convert the total bandwidth into Hertz.
1 GHz is equal to \(10^9\) Hz.

\[ \text{Total Bandwidth in Hz} = 1 \text{ GHz} = 1 \times 10^9 \text{ Hz} \]

### Step 3: Determine the bandwidth required for each channel.
Each telephonic channel requires a bandwidth of 5 kHz. We convert this into Hertz as well.

\[ \text{Bandwidth per channel} = 5 \text{ kHz} = 5 \times 10^3 \text{ Hz} \]

### Step 4: Calculate the number of channels that can be transmitted simultaneously.
To find the number of channels, we divide the total available bandwidth by the bandwidth required for each channel.

\[ \text{Number of channels} = \frac{\text{Total Bandwidth}}{\text{Bandwidth per channel}} = \frac{1 \times 10^9 \text{ Hz}}{5 \times 10^3 \text{ Hz}} \]

### Step 5: Simplify the calculation.
\[ \text{Number of channels} = \frac{1 \times 10^9}{5 \times 10^3} = \frac{10^9}{5 \times 10^3} = \frac{10^9}{5 \times 10^3} = \frac{10^6}{5} = 2 \times 10^5 \]

### Conclusion:
The total number of telephonic channels that can be transmitted simultaneously is:

\[ \text{Number of channels} = 2 \times 10^5 \]