The capacity of batteries such as the typical AA alkaline battery is expressed in units of milliamp-hours (mAh). An AA alkaline battery yields a nominal capacity of 2850 mAh. (b) The starting voltage of a fresh alkaline battery is 1.55 V. The voltage decreases during discharge and is 0.80 V when the battery has delivered its rated capacity. If we assume that the voltage declines linearly as current is withdrawn, estimate the total maximum electrical work the battery could perform during discharge.

Verified step by step guidance

1. Identify the formula for electrical work: \( W = Q \times V_{avg} \), where \( W \) is the work, \( Q \) is the charge, and \( V_{avg} \) is the average voltage.
2. Convert the battery capacity from milliamp-hours (mAh) to coulombs (C). Use the conversion: \( 1 \text{ mAh} = 3.6 \text{ C} \).
3. Calculate the total charge \( Q \) in coulombs by multiplying the capacity in mAh by the conversion factor.
4. Determine the average voltage \( V_{avg} \) during discharge. Since the voltage decreases linearly from 1.55 V to 0.80 V, use the formula for the average of two numbers: \( V_{avg} = \frac{V_{initial} + V_{final}}{2} \).
5. Substitute the values of \( Q \) and \( V_{avg} \) into the formula for electrical work to estimate the total maximum electrical work the battery could perform.

Key Concepts

Electrical Work

Electrical work is defined as the energy transferred by an electric charge moving through a potential difference. It can be calculated using the formula W = V × Q, where W is work, V is voltage, and Q is charge. In the context of batteries, the work done during discharge is the product of the voltage at various points and the total charge delivered, which is derived from the battery's capacity in milliamp-hours.

Battery Capacity

Battery capacity, often measured in milliamp-hours (mAh), indicates the total charge a battery can deliver over time. For example, a battery rated at 2850 mAh can theoretically provide 2850 milliamps for one hour or 1425 milliamps for two hours. Understanding capacity is crucial for estimating how long a battery can power a device and the total charge available for work during discharge.

Voltage Discharge Curve

The voltage discharge curve describes how the voltage of a battery decreases over time as it discharges. In this scenario, it is assumed that the voltage decreases linearly from 1.55 V to 0.80 V as the battery delivers its rated capacity. This linear relationship allows for the estimation of average voltage during discharge, which is essential for calculating the total electrical work performed by the battery.