Question

The energy that will be ideally radiated by a 100 kW transmitter in 1 hour is:

• A. 36 x 10⁷J
• B. 36 x 10⁴J
• C. 36 x 10⁵J
• D. 1 x 10⁵J

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
Power is defined as the rate of energy consumption or radiation per unit time.
Energy (\(E\)) can be calculated by multiplying power (\(P\)) with the total time (\(t\)) for which the transmitter is active.
Key Formula or Approach:
The fundamental relationship is:
\[ E = P \times t \]
Ensure that both power and time are in SI units (Watts and Seconds) before calculation.
Step 2: Detailed Explanation:
1. Convert Power to Watts:
Given power \(P = 100 \text{ kW}\).
\[ P = 100 \times 10^3 \text{ W} = 10^5 \text{ Watts} \]
2. Convert Time to Seconds:
Given time \(t = 1 \text{ hour}\).
\[ t = 1 \times 60 \text{ minutes} \times 60 \text{ seconds} = 3600 \text{ seconds} \]
3. Calculate total Energy:
\[ E = 10^5 \text{ W} \times 3600 \text{ s} \]
\[ E = 3600 \times 10^5 \text{ Joules} \]
\[ E = 36 \times 10^2 \times 10^5 \text{ Joules} \]
\[ E = 36 \times 10^7 \text{ Joules} \]
Step 3: Final Answer:
The total radiated energy is \(36 \times 10^7\) J.