Three resistors having resistances r 1, r 2 and r 3 are connected as shown in the given circuit. The ratio (i3/i1) of currents in terms of resistances used in the circuit is :

Question

Three resistors having resistances r 1, r 2 and r 3 are connected as shown in the given circuit. The ratio (i3/i1) of currents in terms of resistances used in the circuit is : (A) ( r 1/ r 2+ r 3) (B) ( r 2/ r 2+ r 3) (C) (r1/r1+r2) (D) ( r 2/ r 1+ r 3)

Tardigrade Admin · Accepted Answer

( i 2/ i 3)=( r 3/ r 2) and i 2+ i 3= i 1 ( i 2/ i 3)+1=( r 3+ r 2/ r 2) ( i 2+ i 3/ i 3)=( r 2+ r 3/ r 2) ( i 1/ i 3)=( r 2+ r 3/ r 2) ( i 3/ i 1)=( r 2/ r 2+ r 3)

Q. 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 :

$\frac{r _{1}}{r _{2} + r _{3}}$

$\frac{r _{2}}{r _{2} + r _{3}}$

$\frac{r _{1}}{r _{1} + r _{2}}$

$\frac{r _{2}}{r _{1} + r _{3}}$

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

r2​+r3​r1​​

r2​+r3​r2​​

r1​+r2​r1​​

r1​+r3​r2​​

i3​i2​​=r2​r3​​ and i2​+i3​=i1​ i3​i2​​+1=r2​r3​+r2​​ i3​i2​+i3​​=r2​r2​+r3​​ i3​i1​​=r2​r2​+r3​​ i1​i3​​=r2​+r3​r2​​

Q. 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 :

$\frac{r _{1}}{r _{2} + r _{3}}$

$\frac{r _{2}}{r _{2} + r _{3}}$

$\frac{r _{1}}{r _{1} + r _{2}}$

$\frac{r _{2}}{r _{1} + r _{3}}$