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Chapter 1 of 12 • Page 1 of 248🔒 Protected PDF • Watermarked
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ElectricalBasic Electrical
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The watt-hour efficiency of a lead-acid cell varies between

A

25 to 35%

B

40 to 60%

C

70 to 80%

D

90 to 95%

Correct Answer

Concept & PrincipleElectricalBasic Electrical
Option C

70 to 80%

Quick Summary: The watt-hour efficiency (energy efficiency) of a lead-acid cell typically ranges between 70% and 80%. This value represents the ratio of the output energy discharged from the battery to the input energy supplied during the charging process.

💡 Explanation

The watt-hour efficiency (energy efficiency) of a lead-acid cell typically ranges between 70% and 80%. This value represents the ratio of the output energy discharged from the battery to the input energy supplied during the charging process.

🔢 Key Formulas

ηwh=WhoutputWhinput×100\eta_{wh} = \frac{Wh_{output}}{Wh_{input}} \times 100ηwh​=Whinput​Whoutput​​×100

Wh=∫0tV(t)⋅I(t) dtWh = \int_{0}^{t} V(t) \cdot I(t) \, dtWh=∫0t​V(t)⋅I(t)dt

⚙️ Working Principle

The efficiency is limited by internal energy losses, primarily due to internal resistance (I2RI^2RI2R losses) during charge/discharge cycles and electrochemical overpotential requirements. Furthermore, chemical side reactions, such as the electrolysis of water (gassing) during the final stages of charging, consume electrical energy that is not recovered during discharge, leading to energy dissipation as heat.

📌 Key Points
  • ▸

    Watt-hour efficiency accounts for both current (Ampere-hour) efficiency and voltage variations.

  • ▸

    Ampere-hour (Ah) efficiency is higher than watt-hour (Wh) efficiency, typically 85-95%.

  • ▸

    Voltage during discharge is always lower than voltage during charge due to IRIRIR drop and polarization.

  • ▸

    Efficiency is affected by the rate of charge/discharge and the operating temperature.

✅ Advantages
  • ▸

    High reliability for stationary applications.

  • ▸

    Good performance in high-rate discharge conditions.

❌ Disadvantages / Limitations
  • ▸

    Energy loss due to internal resistance.

  • ▸

    Requires careful maintenance to prevent plate sulfation.

🛠️ Applications / Uses
  • ▸

    Automotive starter batteries.

  • ▸

    Uninterruptible Power Supply (UPS) systems.

  • ▸

    Standby power for telecommunication stations.

📄 Additional Information
  • ▸

    Ah efficiency is defined as AhoutAhin\frac{Ah_{out}}{Ah_{in}}Ahin​Ahout​​. Since discharge voltage is lower than charging voltage, ηwh\eta_{wh}ηwh​ is strictly less than ηAh\eta_{Ah}ηAh​.

  • ▸

    Option A (25-35%) is too low; Option B (40-60%) underestimates battery performance; Option D (90-95%) is technically impossible due to thermodynamic losses.

📊 Diagram / Illustration
Watt-Hour Efficiency (ηwₕ)Energy Output (Whᴅᵢₛ꜀ₕₐᵣɢₑᴅ)Energy Input (Wh꜀ₕₐᵣɢₑᴅ)Typical range: 0.70 to 0.80
✅

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

Core Concepts Used
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Electrochemical energy conversion Battery charging/discharging characteristics Efficiency metrics in storage cells
💡 EXAM TIP

Remember that energy efficiency (etaWheta_{Wh}etaWh​) is always lower than charge efficiency (etaAheta_{Ah}etaAh​) because the discharge voltage is inherently lower than the charging voltage.

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