What is the minimum capacity in ampere-hours required for a 50 W emergency transmitter operating for 6 hours with a continuous load?

What is the minimum capacity in ampere-hours required for a 50 W emergency transmitter operating for 6 hours with a continuous load?

• A. A battery rated greater than 177 ampere-hours
• B. A battery rated at least 177 ampere-hours
• C. Both A and B
• D. None of the above

Answer: (C)

To determine the minimum capacity in ampere-hours required for a 50 W emergency transmitter operating for 6 hours with a continuous load, you first calculate the total watt-hours needed. The formula for watt-hours is: \[ \text{Watt-hours} = \text{Power (Watts)} \times \text{Time (Hours)} \] For this scenario: \[ \text{Watt-hours} = 50 \, W \times 6 \, h = 300 \, Wh \] Next, to convert watt-hours to ampere-hours, you need to know the voltage of the system. Assuming a standard voltage, such as 12 volts, the calculation becomes: \[ \text{Ampere-hours} = \frac{\text{Watt-hours}}{\text{Voltage (Volts)}} \] Using 12 volts: \[ \text{Ampere-hours} = \frac{300 \, Wh}{12 \, V} = 25 \, Ah \] However, if the voltage were different, the ampere-hours would vary. Regardless, the context given implies that the minimum capacity should be sufficiently greater than simply fulfilling the immediate power needs for reliability and to account for inefficiencies and battery

To determine the minimum capacity in ampere-hours required for a 50 W emergency transmitter operating for 6 hours with a continuous load, you first calculate the total watt-hours needed.

The formula for watt-hours is:

[ \text{Watt-hours} = \text{Power (Watts)} \times \text{Time (Hours)} ]

For this scenario:

[ \text{Watt-hours} = 50 , W \times 6 , h = 300 , Wh ]

Next, to convert watt-hours to ampere-hours, you need to know the voltage of the system. Assuming a standard voltage, such as 12 volts, the calculation becomes:

[ \text{Ampere-hours} = \frac{\text{Watt-hours}}{\text{Voltage (Volts)}} ]

Using 12 volts:

[ \text{Ampere-hours} = \frac{300 , Wh}{12 , V} = 25 , Ah ]

However, if the voltage were different, the ampere-hours would vary. Regardless, the context given implies that the minimum capacity should be sufficiently greater than simply fulfilling the immediate power needs for reliability and to account for inefficiencies and battery