Question

Study the figures carefully, then calculate the values of E and r.

Answer 1

Let 'E' be the e.m.f. and 'r' be the internal resistance.

Case 1: \[ r = \frac{\mathrm{R} \left( \mathrm{E} - \mathrm{V} \right)}{\mathrm{V}} \]

\[ \therefore r=\frac{1.6(\mathrm{E}-1.6)}{1.6} \] ....(i)

Case 2: \[ r = \frac{\mathrm{R} \left( \mathrm{E} - \mathrm{V} \right)}{\mathrm{V}} \]

\[ r=\frac{3.6(\mathrm{E}-1.8)}{1.8} \] ....(ii)

Comparing (i) and (ii)

\[ \frac{1.6(E-1.6)}{1.6}=\frac{3.6(E-1.8)}{1.8} \]

\[ E-1.6=2(E-1.8) \]

\[ E-1.6=2E-3.6 \]

\[\Rightarrow E=2\text{ V} \]

Substituting the value of E in (i)

\[ r=\frac{1.6(2-1.6)}{1.6}=0.4\ \Omega \]

\[ \therefore E=2\text{ V};\ r=0.4\ \Omega \]