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प्रश्न
Study the figures carefully, then calculate the values of E and r.
संख्यात्मक
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उत्तर
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)
\[ r=\frac{1.6(2-1.6)}{1.6}=0.4\ \Omega \]
\[ \therefore E=2\text{ V};\ r=0.4\ \Omega \]
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