Three resistors having resistances r1, r2 and r3 are connected as shown in the given circuit. The ratio i3i1 of currents in terms of resistances used in the circuit is:

i2i3=r3r2 and i2+i3=i1i2i3+1=r3+r2r2i2+i3i3=r2+r3r2i1i3=r2+r3r2i3i1=r2r2+r3

Three resistors having resistances r1, r2 and r3 are connected as shown in the given circuit. The ratio i3i1 of currents in terms of resistances used in the circuit is:

i2i3=r3r2 and i2+i3=i1i2i3+1=r3+r2r2i2+i3i3=r2+r3r2i1i3=r2+r3r2i3i1=r2r2+r3

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Three resistors having resistances r₁, r₂ and r₃ 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:

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$\frac{r_{2}}{r_{1} + r_{3}}$

$\frac{r_{1}}{r_{2} + r_{3}}$

$\frac{r_{2}}{r_{2} + r_{3}}$

$\frac{r_{1}}{r_{1} + r_{2}}$

answer is C.

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Detailed Solution

$\begin{array}{l} \frac{i_{2}}{i_{3}} = \frac{r_{3}}{r_{2}} and i_{2} + i_{3} = i_{1} \\ \frac{i_{2}}{i_{3}} + 1 = \frac{r_{3} + r_{2}}{r_{2}} \\ \frac{i_{2} + i_{3}}{i_{3}} = \frac{r_{2} + r_{3}}{r_{2}} \\ \frac{i_{1}}{i_{3}} = \frac{r_{2} + r_{3}}{r_{2}} \\ \frac{i_{3}}{i_{1}} = \frac{r_{2}}{r_{2} + r_{3}} \end{array}$