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 :

• A. $\frac{ r _{1}}{ r _{2}+ r _{3}}$
• B. $\frac{ r _{2}}{ r _{2}+ r _{3}}$
• C. $\frac{r_{1}}{r_{1}+r_{2}}$
• D. $\frac{ r _{2}}{ r _{1}+ r _{3}}$

Answer 1

Answer: (B)

$\frac{ i _{2}}{ i _{3}}=\frac{ r _{3}}{ r _{2}} $
and $ i _{2}+ i _{3}= i _{1}$
$\frac{ i _{2}}{ i _{3}}+1=\frac{ r _{3}+ r _{2}}{ r _{2}}$
$\frac{ i _{2}+ i _{3}}{ i _{3}}=\frac{ r _{2}+ r _{3}}{ r _{2}}$
$\frac{ i _{1}}{ i _{3}}=\frac{ r _{2}+ r _{3}}{ r _{2}}$
$\frac{ i _{3}}{ i _{1}}=\frac{ r _{2}}{ r _{2}+ r _{3}}$