Internal Resistance

Resistance is a physical quantity that is the measurement of the ability to resist the flow of electrons or current. The internal resistance of a cell or battery is the resistance offered by it. This occurs due to the presence of ions which obstruct the flow of electrons. It has some specific properties which distinguish it from normal resistance. Unlike the resistance of a conductor, it neither increases with temperature nor has a definite specific resistance. In the following segment, we are going to discuss the pros and cons of it. 

Definition 

The internal resistance of a cell is the ability to resist or restrict the flow of current or electrons. It’s exactly the reciprocal of the conductivity of the cell. An ideal cell will have zero resistance while a normal lithium-ion battery has internal resistance typically between 155m Ohm to 778m Ohm. 

Origin 

The conductivity of any charge carrier is the sum of the product of mobility and electric field and the reciprocal of it gives us the resistance. In a cell, two major charge carriers are electrons and ions. The reciprocal of their total conductivity gives internal resistance. Without those ions it’s impossible to build a battery hence the construction of a battery without internal resistance is impossible. 

Factors affecting internal resistance 

The internal resistance a cell-dependent on the following factors – 

1. It decreases as the mobility of the ions in the battery increases. 
2. It depends on the type and concentration of the electrolyte used. 
3. It is directly proportional to the distance between the electrodes.
4. It is inversely proportional to the area of the electrodes.
5. As temperature increases mobility and drifts velocity of ions increases increasing conductivity and hence internal resistance decreases. 

Function in circuit 

If a cell of emf ‘E’ and internal resistance ‘r’ is connected to an external resistance R in series then – 

Total resistance = R + r 

Hence current in the circuit I = E/(R + r) 

Potential difference across the resistance, 

V = IR = ER/(R+r) 

So, r = (E-V) R/V

With this equation, we can easily find the internal resistance which will help us to find the maximum power output of the circuit. When internal and external resistance has the same value, then we get maximum output power. Maximum output power is given by the equation 

     P = E^2/4r

Power consumed within the cell can be given by the equation – 

         P = E^2 ×r/(R+r) 

In maximum power supply conditions, energy consumed in both internal and external circuits is the same. 

Voltage drop within the cell is called ‘lost voltage’ which can be given by-

      V(lost) = I×r 

Importance 

The internal resistance itself holds no importance in any circuit, but knowing the exact amount of it helps us to construct a circuit with a definite combination of resistance to get maximum power output. We will get maximum power if and only if the external resistance is equal to the internal resistance. 

Problems due to internal resistance 

Due to the presence of internal resistance, we never get the full emf of a cell in the output circuit, decreasing the efficiency of a cell. Also, the internal resistance increases with use decreasing the capacity of a cell. More often the cell ceases to supply power as it becomes too high. It is also one of the causes of heating of mobile phones. 

Conclusion

As time passes by, the cell starts to generate more internal resistance and after a time it becomes so high that the cell ceases to supply power. Above everything, due to the internal resistance, a considerable amount of energy is wasted. Though theoretically, an ideal one will have zero internal resistance, it’s nearly impossible to construct a battery without it. It’s also necessary to know the amount of it to construct a circuit to have maximum power output. The best we can do to solve all the issues is to discover ways to minimise the amount of internal resistance a cell has.