Quiz 4 - Batteries
February 3, 2025
1. Lead-Acid Battery: is commonly used in car starters as shown in
Figure 1.
• Describe how the lead-acid battery gets charged
• While the battery gets charged, does the battery represent a galvanic cell
or an electrolytic cell?
• Determine which electrode is Anode and which electrode is cathode
• Write the half reactions for Anode and Cathode while the battery is being
charged
• Find the minimum voltage at the output of the rectifier, required for
charging the battery
• Let’s assume that the impedance between the rectifier and the battery is
Z = R+jXL = R+jωL where R = 50mΩ and L = 10nH and the battery
voltage is 12V . Calculate the voltage needed at the output of rectifier to
charge the battery with 40A.
2. Nickel-Cadmium (Ni-Cd) Battery: is another rechargeable battery
technology that use nickel and cadmium electrodes in Potassium Hydroxide
(KOH) solution. They are known for their reliability, low maintenance, and
ability to perform in extreme temperatures.
Figure 2 shows the diagram of Nickel-Cadmium battery. The total reaction
of the battery while it’s being discharged (or discharged) is as follows:
Cd + 2N iO(OH) + 2H2 O ⇀
↽ Cd(OH)2 + 2N i(OH)2
The datasheet of a typical Ni-Cd battery (P-120AAS) is provided. The battery’s
C-rate is a measure of how quickly it can charge or discharge relative to its
maximum capacity. A 1C rate means the battery charges (or discharges) in one
hour and a 2C rate means the battery charges (or discharges) in half an hour.
Batteries with a high C-rate are used in power tools (e.g., drills) because they
can handle more power without breaking.
• Find the volumetric and gravimetric energy density of this battery
• What are the battery voltages after half an hour of discharge at a 1C rage
and at 2C rate receptively?
• Draw the equivalent circuit model of the battery (considering Rsc = Rsd ≈
35mΩ)
• Find the amount of losses and efficiency when the battery is discharged
at 2.4A (consider the open circuit voltage of 1.3V in the calculations).
1
Figure 1: Lead-Acid battery in a car starter.
Figure 2: Ni-Cd Battery.