Three resistors having resistances $r_1$, $r_2$ and $r_3$ are connected as shown in the given circuit. The rat

Question

Three resistors having resistances $r_1$, $r_2$ and $r_3$ are connected as shown in the given circuit. The ratio $\frac{i_3}{i_1}$ of currents in terms of resistances used in the circuit is

Accepted Answer

In parallel combination of resistances $r_2$ and $r_3$, potential difference will be equal across both resistance. So, $i_2 r_2 = i_3 r_3 \Rightarrow i_2 = \frac{i_3 r_3}{r_2} \dots(1)$. As per Kirchhoff's first law, $i_1 = i_2 + i_3 \Rightarrow i_1 = (\frac{r_3}{r_2} + 1)i_3 \Rightarrow \frac{i_3}{i_1} = \frac{r_2}{r_2 + r_3}$.

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