Question

If e.m.f of cell is $E$ with internal resistance $r$ and external resistance is $R$ , then terminal voltage will be :

• A. $\frac{Er}{R+r}$
• B. $\frac{ER}{R+r}$
• C. $E$
• D. $\frac{ErR}{R+r}$

Answer 1

The correct option is B $\frac{ER}{R+r}$

The electromotive force (e) or e.m.f. is the energy provided by a cell or battery per coulomb of charge passing through it, it is measured in volts (V). It is equal to the potential difference across the terminals of the cell when no current is flowing.

$\epsilon =\frac{E}{Q}$

where,
$\epsilon$ = electromotive force in volts, V
E = energy in joules, J
Q = charge in coulombs, C

Batteries and cells have an internal resistance (r) which is measures in ohms. When electricity flows round a circuit the internal resistance of the cell itself resists the flow of current and so thermal (heat) energy is wasted in the cell itself.

$\epsilon =I(R+r)$

where,
$\epsilon$ = electromotive force in volts, V
I = current in amperes, A
R = resistance of the load in the circuit in ohms,
r = internal resistance of the cell in ohms.

The above equation can be written as $\epsilon =IR+Irthatis,\epsilon =V+Ir$.

In this equation (V) appears which is the terminal potential difference, measured in volts (V). This is the potential difference across the terminals of the cell when current is flowing in the circuit, it is always less than the e.m.f. of the cell.