The watt-hour efficiency of a lead-acid cell varies between

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70 to 80%

Explanation: The watt-hour efficiency of a lead-acid cell is defined as the ratio of energy output during discharge to the energy input during charge, which typically ranges between 70% and 80%. This value is always lower than the ampere-hour efficiency because the average voltage during discharge is lower than the average voltage during charging due to internal resistance and chemical losses.

Working Principle: During charging, the terminal voltage is higher than the electromotive force (EMF) to overcome internal resistance ($V_{charge} = E + Ir$). Conversely, during discharge, the terminal voltage is lower than the EMF ($V_{discharge} = E - Ir$). Since energy is the product of power and time, the difference in voltage levels across the charging and discharging cycles results in a watt-hour efficiency that is significantly lower than the ampere-hour efficiency (which is typically 85-95%).

Key Formulas: $\eta_{Wh} = \frac{E_{out}}{E_{in}} 	imes 100 = \frac{\int V_{dis} I_{dis} dt}{\int V_{ch} I_{ch} dt} 	imes 100$; $\eta_{Wh} = \eta_{Ah} 	imes \frac{V_{avg, dis}}{V_{avg, ch}}$

Key Points: Ampere-hour (Ah) efficiency is higher than Watt-hour (Wh) efficiency for lead-acid batteries.; Wh efficiency accounts for both current losses and voltage variations during the cycle.; Typical Ah efficiency for lead-acid cells is 85-95%.; Internal resistance ($r$) plays a critical role in reducing Wh efficiency due to $I^2r$ losses.

Advantages: High surge current capability; Relatively low cost per unit of energy storage

Disadvantages: Low energy-to-weight ratio; Requirement for periodic maintenance and ventilation

Applications: Automotive starting, lighting, and ignition (SLI); Uninterruptible Power Supplies (UPS)

Additional Info: The discrepancy between Ah and Wh efficiency arises because $V_{charge} > E > V_{discharge}$.. Option A (25-35%) is too low, while Option D (90-95%) is generally only achieved for Ah efficiency in very high-quality cells.

Answer: C is correct — The watt-hour efficiency of a lead-acid cell typically lies within the range of 70% to 80%.

Exam Tip: Always distinguish between Ampere-hour (Ah) efficiency and Watt-hour (Wh) efficiency; Ah efficiency measures charge capacity, while Wh efficiency measures total energy efficiency.

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