A Survey on Internal Resistance Formula, Explanation & Examples.

According to Thévenin’s theorem, a useful potential difference between the terminals in a linear electric circuit may be described as an ideal voltage source in series with an impedance. This impedance is known as the source’s internal resistance.

When the power source supplies current, the measured voltage output is lower than the no-load voltage; the difference is the voltage drop (the product of current and resistance). Internal resistance is a notion that applies to all forms of electrical sources and is useful for examining many different types of electrical circuits. Cells, EMF and internal resistance are interrelated to one another.

Internal Resistance Formula

Internal resistance is the resistance within a battery or any other voltage source which produces a drop in the source voltage when there is current. It is the barrier to the passage of current provided by the cells and batteries, resulting in heat development. Internal resistance is expressed in the unit Ohms. First, the relationship between internal resistance (r) and cell emf (e)is given.

e = I (r + R)

Here e is the electromotive force ( expressed in Volts), R is the load resistance, I is the current  and r is the cell’s internal resistance, measured in ohm.

Rearranging the preceding equation yields, 

e = IR + Ir 

According to Ohm’s law, V=IR. Substituting for IR we get,

e = V + Ir 

When the current (I) flows through the circuit, V is the potential difference between the terminals across the cell in the preceding equation.

The emf (e) of a cell is always bigger than the potential difference between the terminal across the cell.

Example: When no current runs through the circuit, the potential difference across the cell is 3 V. The terminal potential difference reduces to 2.8 Volts while the current I = 0.37 Ampere flows. What is the cell’s internal resistance (r)?

Solution:

e = V + Ir

Or, e – V = Ir

Or, (e – V)/I = r

Therefore, r = (3.0 – 2.8)/0.37 = 0.54 Ohm. 

The electrons flowing through the cell convert part of the electrical energy to heat energy due to the cell’s internal resistance. As a result, the potential difference available to the rest of the circuit is as follows.

V = E (EMF of a cell) – Ir (the p.d. across the internal resistor).

Internal resistance is provided by the electrodes and electrolyte, which oppose the passage of current within the cell.

Thévenin’s theorem

Thévenin’s theorem, originally stated in terms of only direct-current resistive circuits, states that “any linear electrical network containing only voltage sources, current sources and resistances can be replaced at terminals A and B with a combination of equivalent voltage source Vth in a series connection with a resistance Rth.” In-circuit theory terms, it allows any one-port network to be diminished to a single voltage source and impedance.

Applications of Internal resistance:

Internal Resistance is significant to investigate in the following ways:

It can be applied to enhance the efficiency of an electric motor or any other electrical equipment, it is necessary to first understand how much Internal Resistance it has and how it may be lowered.

When studying the Internal Resistance of batteries, the term “Internal Resistance” is used. Internal resistance is a fundamental concept in electrical engineering that may be used in a wide range of projects and experiments using electricity.

Internal Resistance is especially important for constructing engines for automobiles, trucks and other big vehicles. Internal Resistance (IR) can be used in Internal Combustion Engines (ICE) to increase engine performance and fuel efficiency.

Conclusion

The Internal Resistance Formula is a notion that may be applied to a wide range of engines and electrical equipment. Internal Resistance Formulas are grasped in their most basic form before moving to more complex applications. Internal Resistance Formula is used in various ways, but it is critical to understand where and how Internal Resistance should be used. Internal Resistance is most commonly utilised in electric motors and electrical equipment but can be used to investigate the Internal Resistance of batteries. This article will help to give you an excellent idea about the concept of internal resistance and the relationship between internal resistance (r) and emf (e) of cells.