Define emf, terminal potential difference, and internal resistance. Derive the relation between them for the circuit drawing current.

Electromotive force (emf):

The electromotive force of a source is defined as the work done in moving a unit positive charge through the source from lower potential to the higher potential end. The emf is independent to the internal resistance (r)/ Emf is denoted as (E) and is given as

\(E=\frac Wq\)

Where W is the work done to carry the magnitude of charge q. Its Si unit is the joule per coulomb (j/C)

Terminal Potential Difference

The work done in bringing a unit charge from one point to another point in the external circuit is called the potential difference between the points. It is denoted as V and given as

\(V=\frac{W}{q_0}\)

Where W is the work done to carry the magnitude of the charge q₀ 

Click here to check the difference between emf and potential difference (pd)

Internal Resistance of the cell

The resistance offered by a cell (source of emf) is called the internal resistance of the cell. It is due to the electrolyte and electrodes of the cell. It is generally denoted by r and measured in ohms.

Relation between emf, Internal Resistance, and the Terminal pd of the cell

Let E be the emf of a cell, r be its internal resistance and R be the external resistor connected in series with the cell. V is a voltmeter that measures the potential difference between two points A and B of the circuit. S is the switch, when the circuit is open, no current flows through the circuit. The reading of the voltmeter gives (emf) E of the cell. When the circuit is closed, the current I flowing the circuit is given by

\(I=\frac{E}{R+r}\) ------ (i)

Or, E = It + It ------- (ii)

Terminal potential difference (pd), V = potential difference across the external resistance

Or, V = IR ------- (iii)

From the  equations (ii) and (iii), we can write, E = V + Ir

Or, V = E- Ir ------- (iv)

Where Ir is the potential drop across the internal resistance of the cell. This is the required relationship between E, V, and r