Question

A cell of e.m.f. $\epsilon$ and internal resistance $r$ is used to send current to an external resistance $R$. The expressions for the potential difference across the cell is :

• A. $\frac{\epsilon }{(R+r)}\times R$
• B. $\frac{\epsilon }{(R+r)}\times r$
• C. $\frac{\epsilon }{(R+r)}\times Rr$
• D. $\frac{\epsilon }{(R+r)}\times 2r$

Answer 1

Answer: (A)

$\frac{\epsilon }{(R+r)}\times R$

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 $I=\frac{\epsilon }{R+r}$.
Hence, the expression for the current drawn from the cell is $I=\frac{\epsilon }{R+r}$.

Ohm's law states that the current through a conductor between two points is directly proportional to the potential difference across the two points.

Introducing the constant of proportionality, the resistance, we arrive at the usual mathematical equation that describes this relationship: $I=\frac{V}{R}$,where, I is the current through the conductor in units of amperes, V is the potential difference measured across the conductor in units of volts, and R is the resistance of the conductor in units of ohms.

Therefore, $V=IR.$

Substituting the expression for I in the above equation, gives the total potential difference in the circuit. That is,

$V=\frac{\epsilon }{R+r}\times R$.

Hence, the potential difference across the cell is $V=\frac{\epsilon }{R+r}\times R$.