Hi friends, in this article, I am discussing about the lead acid battery charging and discharging equations and hope you will find it informative and helpful.
 
A lead-acid battery is the most inexpensive battery and is widely used for commercial purposes. It consists of a number of lead-acid cells connected in series, parallel or series-parallel combination.
 
A lead-acid cell basically contains two plates immersed in electrolyte (dilute sulphuric acid i.e. H2SO4 of specific gravity about 1.28). The positive plate (anode) is made up of lead-peroxide (PbO2) and the negative plate (cathode) is made up of sponge lead (Pb).
 
When the cell is delivering electrical energy to the external circuit (load), the process is known as discharging of the cell. Whereas, when it is taking electrical energy from the external DC source, the process is known as charging of the cell.
 

Lead acid battery charging and discharging equations

 

Lead acid battery discharging equations

 
lead acid battery charging and discharging equations
 
When the sulphuric acid is dissolved, its molecules are dissociated into hydrogen ions (2H+) and sulfate ions (SO4– –) which moves freely in the electrolyte.
 
When the load resistance is connected to terminals of the battery; the sulfate ions (SO4– –) travel towards the cathode and hydrogen ions (2H+) travel towards the anode. The chemical reactions at the cathode are as under:
 
At cathode
 
SO4– –  – 2e = SO4 (radical)
Pb + SO4  —–> PbSO4
 
At anode
 
Each hydrogen ion (H+) on reaching the anode, takes one electron from it to become hydrogen gas. This electron is the same electron which is given by the sulfate ion at the cathode and has come to the anode via external load resistor R.
 
2H+ + 2e = 2H
 
The hydrogen gas liberated at the anode acts chemically on the anode material (PbO2).
 
PbO2 + 2H —-> PbO + H2O
 
This PbO2 is reduced to PbO which reacts with H2SO4 and forms PbSO4.
 
Thus during discharging
 

  • Both the plates are transformed into lead sulfate (PbSO4).
  • Sulphuric acid is consumed and water is formed which reduces the specific gravity of electrolyte from 1.28 to 1.18.
  • The terminal voltage of each battery cell falls to 1.8V.
  • Chemical energy is converted into electrical energy which is delivered to load.

Lead acid battery charging equations

 
The lead-acid battery can be recharged when it is fully discharged. For recharging, positive terminal of DC source is connected to positive terminal of the battery (anode) and negative terminal of DC source is connected to the negative terminal (cathode) of the battery.
 
During recharging, hydrogen ions (2H+) travel towards the cathode and sulfate ions (SO4– –) travel towards the anode. The chemical reactions are as under:
 
At anode
 
SO4– –  – 2e —> SO4 (radical)
SO4 + H2O —> H2SO4 + O
 
The oxygen (in atomic stage) reacts chemically with anode material (PbSO4):
 
PbSO4 + O + H2O —> PbO2 + H2SO4
 
At cathode
 
Each hydrogen ion (H+) on reaching the cathode, takes one electron from it to become hydrogen gas. This electron is given by sulfate ion at the anode and has come to cathode via external circuit (from the DC source)
 
2H+ + 2e —> 2H
 
The hydrogen gas liberated at the cathode acts chemically on the cathode material (PbSO4)
 
PbSO4 + 2H —> Pb + H2SO4
 
Thus, PbSO4 is transformed to Pb. Water (H2O) is consumed and H2SO4 is formed in above chemical reactions. This increases the specific gravity of the electrolyte. Ultimately, the cell regains its previous (before discharging) chemical compositions.
 
Thus during charging

  • The anode is transformed into lead peroxide (PbO2) and cathode into the spongy lead (Pb).
  • Water is consumed and sulphuric acid is formed which increases the specific gravity of electrolyte from 1.18 to 1.28.
  • The terminal voltage of each battery cell increases to 2.2 to 2.5V.
  • Electrical energy is converted into chemical energy which is stored in the cell.

 
Thanks for reading about lead acid battery charging and discharging equations.
 

AC Fundamentals – 3 | Objective Type Question Answers

#1 Power factor of magnetizing component of current of a transformer is

zero

#2 In a R-L-C circuit

all above are correct

#3 Physical quantities of resistance, inductance and capacitance are represented by R, L and C respectively. The combinations which have dimensions of frequency are

1/√(LC)

#4 In RLC series resonant circuit magnitude of resonance frequency can be changed by changing the value of

L or C

#5 In a series L- C circuit at the resonant frequency the

current is maximum

#6 In a RLC series circuit if voltage across the circuit is reduced to half the current will change to

current/2

#7 The time constant of a series R-C circuit is given by

RC

#8 If resistance is 200 ohms and inductance is 2H in a R-L series circuit, then time constant of this circuit will be

0.1 s

#9 Which of the following coil will have large resonant frequency ?

A coil with large distributed capacitance

#10 The safest value of current the human body can carry for more than 3 second is

9 mA

#11 A pure inductance connected across 250 V, 50 Hz supply consumes 100 W. This consumption can be attributed to

the statement given is false

#12 In an A.C. circuit, a low value of kVAR compared with kW indicates

high power factor

#13 In A.C. circuits, laminated iron is invariably used in order to

reduce eddy current loss

#14 The apparent power drawn by an AC. circuit is 10 kVA and active power is 8 kW. The reactive power in the circuit is

6 kVAR

#15 The reactance offered by a capacitor to alternating current of frequency 50 Hz is 20 Ω. If the frequency is increased to 100 Hz, reactance becomes

10 Ω

#16 What will be the phase angle between two alternating waves of equal frequency, when one wave attains maximum value the other is at zero value?

90

#17 The purpose of a parallel circuit resonance is to magnify

voltage

#18 At very low frequencies a series R-C circuit behaves as almost purely

capacitive

#19 Skin effect occurs when a conductor carries current at ……………. frequencies.

high

#20 At ………….. frequencies the parallel R-L circuit behaves as purely resistive.

very high

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