2021 Current ElectricityCombination of Resistors – Current Division Medium Question 38 of 130 in Current Electricity

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:

A $\frac{r_2}{r_2+r_3}$
B $\frac{r_1}{r_1+r_2}$
C $\frac{r_2}{r_1+r_3}$
D $\frac{r_1}{r_2+r_3}$

The answer is A.

Solution


$r_2$ and $r_3$ are in parallel (same potential difference), so $i \propto \frac{1}{r}$: $\frac{i_2}{i_3} = \frac{r_3}{r_2}$
$i_1 = i_2 + i_3 \Rightarrow i_3 = \frac{r_2}{r_2 + r_3}i_1$
$\frac{i_3}{i_1} = \frac{r_2}{r_2 + r_3}$

Concept current ratio in a parallel branch

Current Electricity in past papers

130 questions from this chapter have appeared across 27 exam years.