Current Electricity
5.0 Electromotive force $\left( \xi \right)$
5.0 Electromotive force $\left( \xi \right)$
The electromotive force (EMF) of a source is the work done by the source in taking a unit positive charge once around the complete circuit. $$\xi = \frac{W}{q}$$
It is equal to the maximum potential difference between the two terminals of the source when it is an open circuit.
It is represented by $\left( \xi \right)$.
SI unit is Volt $(V)$.
Terminal potential difference
The potential drop across the terminals of a cell when a current is being drawn from it is called terminal potential difference.
In other words, the potential drop across $AB$ is known as the terminal potential difference when a current is being drawn from the cell.
SI unit is Volt $(V)$.
Internal resistance of cell ($r$)
The resistance offered by the electrolyte of a cell to the flow of current between its electrodes is called internal resistance of the cell.
The internal resistance of the cell is represented by '$r$'.
Internal resistance of a cell,
- Depends on nature of electrolyte.
- Increases with increase in the concentration of electrolyte.
- Increases with increase in distance between electrodes.
- Decreases with increase in area of electodes immersed in the electrolyte.
- Increases with decrease in temperature of electrolyte.
Relation between ($\xi $), ($V$) and ($r$)
EMF ($\xi $) is the work done by cell in carrying unit charge along the closed path.
Work done in carrying unit charge from $A$ to $B$ against external resistance $R$ is same as the work done in carrying unit charge from $B$ to $A$ against an internal resistance $r$.
or, $$\xi ={V_R}+{V_r}$$
By ohm's law, $$\begin{equation} \begin{aligned} \Rightarrow {V_R} = IR \\ \Rightarrow {V_r} = Ir \\\end{aligned} \end{equation} $$
Therefore, $$\xi = IR + Ir = I\left( {R + r{\text{ }}} \right)$$
Hence the current in circuit is$$I = \frac{\xi }{{\left( {R + r} \right)}}$$
Terminal potential difference,$${V = IR = \frac{{\xi R}}{{R + r}}}$$
or,$$V = \xi - Ir$$
Note:
(i)The potential difference across terminal of the cell in open circuit is equal to its emf. If when $I = 0$, we have ${V_{open}} = \xi $
(ii) The potential difference across terminal of cell in closed circuit is always less than its emf. $V < \xi $
