Three resistors having resistances- r1-r2 and r3 are connected as shown in the given circuit- The ratio i3 i1 of currents in terms of resistances used in the circuit is -

In parallel combination of resistances r_2 and nbsp;r_3, potential difference will be equal across both resistances. nbsp; So, i_2r_2=i_3r_3⇒ i_2=r_3r_2i ...

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Standard XII

Physics

Resistors in Series and Parallel

Three resisto...

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 -

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

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

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

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

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Solution

The correct option is C $\frac{r_{2}}{r_{2} + r_{3}}$

In parallel combination of resistances $r_{2}$ and $r_{3}$ , potential difference will be equal across both resistances.

So,

$i_{2} r_{2} = i_{3} r_{3} \Rightarrow i_{2} = \frac{r_{3}}{r_{2}} i_{3} . . . (1)$

Also,

$i_{1} = i_{2} + i_{3}$

$\Rightarrow i_{1} = (\frac{r_{3}}{r_{2}} + 1) i_{3} [From equation 1]$

$\Rightarrow \frac{i_{3}}{i_{1}} = \frac{r_{2}}{r_{2} + r_{3}}$

Hence, option $(C)$ is the correct answer.

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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 -

The correct option is C r2r2+r3 In parallel combination of resistances r2 and r3, potential difference will be equal across both resistances. So, i2r2=i3r3⇒i2=r3r2i3 ...(1) Also, i1=i2+i3 ⇒i1=(r3r2+1)i3 [From equation 1] ⇒i3i1=r2r2+r3 Hence, option (C) is the correct answer.

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 -