The current through a \( 4/3\,\Omega \) external resistance connected to a parallel combination of two cells of 2 V and 1 V emf and internal resistances of \( 1\,\Omega \) and \( 2\,\Omega \) respectively is ___________.
Fill in the blank with the correct answer from the options given below.
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 5/6 A
Two cells in parallel act as a single cell whose equivalent emf and internal resistance are
\( \displaystyle \varepsilon_{\mathrm{eq}} = \frac{\varepsilon_1 r_2 + \varepsilon_2 r_1}{r_1 + r_2} \qquad r_{\mathrm{eq}} = \frac{r_1 r_2}{r_1 + r_2} \)
\( \varepsilon_1 = 2\,\mathrm{V},\ r_1 = 1\,\Omega \)
\( \varepsilon_2 = 1\,\mathrm{V},\ r_2 = 2\,\Omega \)
\( \displaystyle \varepsilon_{\mathrm{eq}} = \frac{2 \times 2 + 1 \times 1}{1 + 2} = \frac{5}{3}\,\mathrm{V} \qquad r_{\mathrm{eq}} = \frac{1 \times 2}{1 + 2} = \frac{2}{3}\,\Omega \)
This equivalent cell drives the current through the external resistance \( R = 4/3\,\Omega \):
\( \displaystyle I = \frac{\varepsilon_{\mathrm{eq}}}{R + r_{\mathrm{eq}}} = \frac{5/3}{4/3 + 2/3} = \frac{5/3}{2} = \frac{5}{6}\,\mathrm{A} \)