## Internal resistance formula

Ohms are used to measure internal resistance. The connection between internal resistance (r) and electromotive force (e) in cells is given by.

I (r + R) = e

Where e is the electromotive force (Volts), I is the current (A), R is the load resistance, and r is the cell’s internal resistance in ohms.

e = V + Ir (or e = IR + Ir)

V is the potential difference (terminal) across the cell while the current (I) is flowing through the circuit in the equation above.

The following is the connection between Internal Resistance represented by r and emf denoted by e of a cell:

I (r + R) = e

Where we can see that the quantity symbolised by the letter e = EMF, also known as the electromotive force of Volts, is expressed as: I = current, denoted by A, R = Load resistance, and r is the Internal resistance of a cell measured in ohms.

Rearranging the equation above yields the following:

In other words, e = IR + Ir or e = V + Ir.

Note that a cell’s emf (e) is always bigger than the cell’s potential difference (terminal).

## Example

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

**Solution:**

V + Ir = e

Alternatively, e – V = Ir

Alternatively, (e – V)/I = r

r = (3.0 – 2.8)/0.37 = 0.54 Ohm as a result.

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 accessible to the circuit as a whole is:

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

**2. When no current runs through the circuit, this is the potential difference across the cell, which is 3 V. The terminal potential difference reduces to 2.8 Volts while the current dedicated by I = 0.37, which is ampere, is flowing. Determine the cell’s internal resistance, represented by the letter r.**

**Solution:**

In other words, e = V + Ir.

Alternatively, we can see e – V = Ir.

Alternatively, (e – V)/I = r

As a result, we have r = (3.0 – 2.8)/0.37 = 0.54 Ohm.

Now, due to the cell’s internal resistance, which is the electrons passing through the cell, some of the electrical energy is converted to heat energy.