Three resistors having resistances r _ 1 , r _ 2 and r _ 3 are connected as shown in the given circuit. The ratio i _ 3 i _ 1 of currents in terms of resistances used in the circuit is :

NEET 2021

Exam: NEET
Year: 2021
Subject: Physics
Chapter: Current Electricity

NEET 2021 · Physics · Current Electricity

Three resistors having resistances r _ 1 , r _ 2 and r _ 3 are...

Three resistors having resistances ${r}_{1}, {r}_{2}$ and ${r}_{3}$ are connected as shown in the given circuit. The ratio $\dfrac{{i}_{3}}{{i}_{1}}$ of currents in terms of resistances used in the circuit is :

Three resistors having resistances r _ 1 , r _ 2 and r _ 3 are connected as shown in the given circuit. The ratio i _ 3

Options

A $\dfrac{{r}_{1}}{{r}_{2} + {r}_{3}}$
B $\dfrac{{r}_{2}}{{r}_{2} + {r}_{3}}$
C $\dfrac{{r}_{1}}{{r}_{1} + {r}_{2}}$
D $\dfrac{{r}_{1}}{{r}_{1} + {r}_{2}}$ .

Correct answer

B. $\dfrac{{r}_{2}}{{r}_{2} + {r}_{3}}$

Step-by-step solution

Three resistors having resistances r _ 1 , r _ 2 and r _ 3 are connected as shown in the given circuit. The ratio i _ 3

Potential difference between $B$ and $C$ ,

${V}_{BC} = {i}_{3}{r}_{3} = {i}_{1} \times \dfrac{{r}_{2}{r}_{3}}{{r}_{2} + {r}_{3}}$

$⇒ {i}_{3} = {i}_{1} \times \dfrac{{r}_{2}}{{r}_{2} + {r}_{3}}$

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