Question

A cell of e.m.f. 1.5 V, records a p.d. of 1.0 V, when connected to an external resistance R, such that current flowing through the circuit is 0.4 A. Calculate the value of R and the internal resistance of the cell.

Answer 1

E = 1.5 V; V = 1.0 V; I = 0.4 A; R = ?

By Ohm’s law, \[ \text{I} = \frac{\text{V}}{\text{R}} \]

\[ \therefore \text{R}=\frac{\text{V}}{\text{I}}\]

\[=\frac{1.0}{0.4}\]

= 2.5 Ω

Also, \[ \text{I} = \frac{\text{E}}{\text{R} + r} \]

\[ \Rightarrow 0.4 = \frac{1.5}{2.5 + r} \]

\[\Rightarrow 1 + 0.4r = 1.5 \]

\[ \Rightarrow 0.4r = 0.5 \]

\[r=\frac{0.5}{0.4}\]

\[ \therefore r=1.25 \Omega\]