Final answer:
The duration batteries must sustain power during an electrical outage depends on the power requirements and the battery specifications. Using the example of a 1.00 Ah and 1.58 V alkaline battery powering a 1.00-W bulb, the battery life can be estimated to be around 1.59 hours. Off-grid systems may require much longer battery life based on facility needs.
Step-by-step explanation:
The duration for which batteries must sustain power during an electrical outage can vary depending on the application and requirements for the facility in question. To determine this duration, one needs to consider factors such as the wattage of the devices being powered, the voltage and ampere-hour (Ah) rating of the batteries, and the facility’s power needs. Taking the example of an alkaline battery rated at 1.00 Ah and 1.58 V sustaining a 1.00-W flashlight bulb, we can calculate the battery's life. Given that power (P) is the product of current (I) and voltage (V), and we know that P = 1.00 W and V = 1.58 V, the current can be calculated as I = P/V. Therefore, I = 1.00 W / 1.58 V ≈ 0.63 A. To find out how long the battery can last, we use the ampere-hour rating: battery life in hours = Ah rating / current. This results in approximately 1.00 Ah / 0.63 A ≈ 1.59 hours of battery life.
It is important to note that in actual applications, the time that batteries can sustain power will also depend on the efficiency of the battery, its age, temperature, and the discharge rate. Moreover, off-grid battery systems designed for backup power may need to accommodate the power demands for a much longer duration, potentially several hours to days, depending on the critical nature of the facility and its operations.