Height of the receiving and transmitting antenna in communication of a signal are 245 m and 180 m respectively. Find the maximum distance between the two antennas for proper communication.
- 104 km
- 208 km
- 52 km
- 96 km
The Correct Option is A
Solution and Explanation
Understanding the Problem
We need to find the maximum distance in the line of sight between two antennas using the formula:
\( d = \sqrt{2Rh_t + 2Rh_r} \)
where:
- \( R = 6400 \, \text{km} \) (radius of the Earth)
- \( h_t = 180 \, \text{m} \) (height of the transmitting antenna)
- \( h_r = 245 \, \text{m} \) (height of the receiving antenna)
Corrected Solution
1. Convert Units:
Since \(R\) is in kilometers, we need to convert \(h_t\) and \(h_r\) to kilometers.
\( h_t = 180 \, \text{m} = 0.18 \, \text{km} \)
\( h_r = 245 \, \text{m} = 0.245 \, \text{km} \)
2. Substitute Values into the Formula:
\( d = \sqrt{2(6400)(0.18) + 2(6400)(0.245)} \)
\( d = \sqrt{2(6400)(0.18 + 0.245)} \)
\( d = \sqrt{12800(0.425)} \)
\( d = \sqrt{5440} \)
3. Calculate the Distance:
\( d \approx 73.76 \, \text{km} \)
Error in Your Calculation
You directly added the heights in meters and multiplied them by the radius in kilometers without converting the heights to kilometers. This led to a significantly larger and incorrect result.
Final Answer
The maximum distance in the line of sight between the two antennas is approximately \( 73.76 \, \text{km} \).
Top Questions on communication systems
- VHF waves travel as _______.
- AP PGECET - 2025
- Electronics and Communication Engineering
- communication systems
- Commercial band for FM broadcasting is ________.
- AP PGECET - 2025
- Electronics and Communication Engineering
- communication systems
- The movement of charge carriers due to charge carrier concentration gradient is called ________.
- AP PGECET - 2025
- Electronics and Communication Engineering
- communication systems
- A narrow band FM signal is generated using a phase modulator. The maximum deviation at the output of a phase modulator is about________.
- AP PGECET - 2025
- Electronics and Communication Engineering
- communication systems
- To save transmitted power, the carrier of an AM signal obtained by sinusoidal modulation to a depth of modulation equal to 1, has been recovered. The percentage saving in power is________.
- AP PGECET - 2025
- Electronics and Communication Engineering
- communication systems
Questions Asked in JEE Main exam
- A bar magnet has total length \( 2l = 20 \) units and the field point \( P \) is at a distance \( d = 10 \) units from the centre of the magnet. If the relative uncertainty of length measurement is 1%, then the uncertainty of the magnetic field at point P is:
- JEE Main - 2025
- Magnetic Field
- A force of 49 N acts tangentially at the highest point of a sphere (solid of mass 20 kg) kept on a rough horizontal plane. If the sphere rolls without slipping, then the acceleration of the center of the sphere is:
- JEE Main - 2025
- Quantum Mechanics
Let $ P_n = \alpha^n + \beta^n $, $ n \in \mathbb{N} $. If $ P_{10} = 123,\ P_9 = 76,\ P_8 = 47 $ and $ P_1 = 1 $, then the quadratic equation having roots $ \alpha $ and $ \frac{1}{\beta} $ is:
- JEE Main - 2025
- Relations and functions
- If \( \alpha + i\beta \) and \( \gamma + i\delta \) are the roots of the equation \( x^2 - (3-2i)x - (2i-2) = 0 \), \( i = \sqrt{-1} \), then \( \alpha\gamma + \beta\delta \) is equal to:
- JEE Main - 2025
- Complex numbers
- The sum of all local minimum values of the function \( f(x) \) as defined below is:
\[ f(x) = \begin{cases} 1 - 2x & \text{if } x < -1, \\[10pt] \frac{1}{3}(7 + 2|x|) & \text{if } -1 \leq x \leq 2, \\[10pt] \frac{11}{18}(x-4)(x-5) & \text{if } x > 2. \end{cases} \]- JEE Main - 2025
- Functions
Concepts Used:
Communication Systems
A system that describes the information exchange between two points is called the communication system. The transmission and reception process of information is called communication. The major elements of communication are such as:
- The Transmitter of information
- Channel or medium of communication
- The Receiver of information
Examples Of Communication Systems:
The following are the examples of communication systems:
- Internet
- Public Switched Telephone network
- Intranet and Extranet
- Television
Types Of Communication Systems:
Turning on Signal specification or technology, the communication system is categorized as follows:
- Analog technology communicates data as electronic signals of differing frequencies or amplitude. For instance Broadcast and telephone transmission.
- In Digital technology, the data are created and processed in two states: High (represented as 1) and Low (represented as 0). Also this technology stores and transmits data in the form of 1's and 0's.
Elements of a Communication System:
