Question

A cell of emf ‘E’ and internal resistance ‘r’ is connected across a variable load resistor R. Draw the plots of the terminal voltage V versus (i) R and (ii) the current I.

Answer 1

(i) Current in circuit \(I=\frac{\epsilon}{R+r}\)

Terminal potential difference

\(V=IR=(\frac{\epsilon}{R+r})R\)

= \(\frac{\epsilon}{(R+r)/R}=\frac{\epsilon}{1+\frac{r}{R}}\)

When R increases r/R decreases, so terminal potential difference increases with the increase of R.

When R = 0, V → 0

When R = r, V = \(\frac{\epsilon}{2}\)

When R → ∞ (open circuit), V = ε 

The graph of terminal potential difference V versus R is shown in figure.

(ii) V = E - Ir \(\Rightarrow I=\frac{E\,-\,V}{r}\)