CBSE Class 12 · 2009 · Current ElectricityShort Answer

A cell of EMF

E

and internal resistance

r

is connected across a variable resistor

R

. Plot a graph showing the variation of the terminal potential difference

V

with

R

, and predict from the graph the condition under which

V

becomes equal to

E

Answer: $V = \frac{E R}{R + r}$ ; the graph rises and saturates towards $E$ . $V \to E$ when $R \to \infty$ (open circuit / no current).

Solution

V = E - I r = E - \frac{V}{R} r \Rightarrow V (1 + \frac{r}{R}) = E \Rightarrow V = \frac{E R}{R + r}

. As

R

increases,

V

increases and approaches

E

asymptotically; it equals

E

only in the limit

R \to \infty

, when no current is drawn.

CBSE Class 12 Board · 2009 · Subjective