Why is the terminal voltage less than EMF during discharging of battery?

The equivalent circuit of the battery is as given below. A voltage source can be represented as EMF source with an internal series resistance.
battery cell under load
Under no load condition, the current flowing through the battery or cell is zero, and the terminal voltage is exactly equal to the EMF of cell or battery.
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When the cell or battery is connected to the load, the battery supplies current to the load. Now, if we measure the voltage across the load ( that is the same point at battery terminals), the measured voltage will be somewhat less than the battery EMF. The measured voltage at the terminal of battery when battery supplies current to load is called the terminal voltage.
What is the reason of reduction in the battery voltage? There must be some voltage drop inside the battery. Yes, the voltage drop takes place inside the cell because of the internal resistance of the battery. The internal resistance of the voltage source is zero for an ideal voltage source.However, the voltage source can never be an ideal source and its internal resistance can not be zero. The internal resistance of the battery or cell can be made as minimum as possible by selecting the proper metallurgy for the battery materials. 

The voltage source has some internal resistance which cause the voltage drop during discharging of the battery, and terminal voltage will be less than the EMF of the battery at the time of discharging. Does the terminal voltage is same for all types of loads? No it depends upon the value of the load. The higher the value of the load, the more will be the current from battery and consequently terminal voltage will be less. Let us understand this phenomenon with the Kirchhoff’s voltage law.

simple model of cell

In the above circuit, the load is infinitive and the current flowing through the battery is zero. The voltage drop across the internal resistance is ILRis equal to zero because Iis zero, and in this condition the battery is said to be open circuited. In open circuited condition, the battery terminal voltage is equal to the EMF of the battery.

The cell voltage having EMF V is connected to the load RL. The cell supplies current IL to the load. According to Kirchhoff’s voltage law sum of the potential drops in a closed loop electric circuit is zero.

V = ILRs + ILRL
V = ILRs + (VT/RL) RL
V = ILRs + VT     

If  battery is open circuit,IL = 0
V =ILRs + ILRL
V=0 x Rs + (VT/RL) RL
V=0 + V
V  =V

When the battery is not connected to the load the load current is zero and battery EMF is equal to the terminal voltage. 

Now if the load is connected to the battery, the battery starts supplying the current to the load.

V = ILRs + ILRL
V = ILRs + (VT/RL) RL
V = ILRs + V
V= V- ILRs

From above, it is clear that the terminal VT voltage is less than the EMF of battery. The reason of less terminal voltage when battery is under load is voltage drop inside the battery caused by battery internal resistance Rs.   

The terminal voltage is further depends on the magnitude of the load. The load current depends on the value of the load resistance. The lower value of load resistance causes to draw more current from the battery, and consequently the more voltage drop takes place inside the battery, and there will be less terminal voltage. Let us understand this with illustrative example.

battery terminal voltage

Case 1: When battery is under no load

When there is no current flowing through the battery, the terminal voltage is equal to the battery EMF. The battery EMF is 9 volts and the terminal voltage is equal to battery EMF that is 9 volts.

Case 2: When battery is under load – Load is 9 Ω

When the battery of 9 volts EMF is connected to 9 Ω resistance the battery will supply 1.49 amp. current to the circuit and the terminal voltage is 8.94 volts. The voltage drop across the internal resistance of the battery is 0.015 volts.

Case 3: When battery is under load – Load is 6 Ω

When the battery of 9 volts EMF is connected to 6 Ω resistance the battery will supply 0.99 amp. current to the circuit and the terminal voltage is 8.91 volts.The voltage drop across the internal resistance of the battery is 0.001 volts.

From above, it is clear that voltage drop across the internal resistance increases with increase in the current. 

When there is no current flowing through the battery, the terminal voltage is equal to the battery EMF. The battery EMF is 9 volts and the terminal voltage is equal to battery EMF that is 9 volts.

The terminal voltage decrease with increase of load current or the current through the battery.The graph showing relationship between voltage and current is as shown below.

Why is the terminal voltage less than EMF during discharging

Illustrative Example:

A battery has 9 volts emf and internal resistance of 0.1 Ohms. Calculate
a) Calculate battery terminal voltage when it is connected to 15 Ohms load.
b) The terminal voltage when it is connected to 1.0 Ohms load.

solved problem on battery terminal voltage

b) When battery is connected to 1.0 Ohms load

battery terminal voltage under load- solved problem

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