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: \( r_1 \)<\text{>\( r_2 \)<\text{>\( r_3 \)<\text{>\( i_1 \)<\text{>\( i_3 \)<\text{>

From the circuit diagram, the current \( i_1 \) splits into two parallel branches containing resistors \( r_2 \) and \( r_3 \). Let the currents in the branches containing \( r_2 \) and \( r_3 \) be \( i_2 \) and \( i_3 \) respectively (where \( i_3 \) is the current through \( r_3 \)). Using the current division rule, the current through resistor \( r_3 \) is given by: \[ i_3 = i_1 ( \frac{r_2}{r_2 + r_3} ) \]\nTherefore, the ratio of currents is: \[ \frac{i_3}{i_1} = \frac{r_2}{r_2 + r_3} \]