# An electric current is passed through a circuit  containing two wires of the same material, connected in parallel. If the lengths and radii of the wires are in the ratio of 4/3 and 2/3    then the ratio of the currents passing through the wire will be Option 1) $3$ Option 2) $1/3$ Option 3) $8/9$ Option 4) $2$

Answers (2)
N neha
S Sabhrant Ambastha

As we learnt in

Resistivity -

$R=\rho\frac{l}{A}$

- wherein

$\rho\rightarrow$  resistivity / specific resistance

$V=I_{1}R_{1}=I_{1}\:\rho\frac{l_{1}}{\pi r_{1}^{2}}$

$V=I_{2}R_{2}=I_{2}\:\rho\frac{l_{1}}{\pi r_{2}^{2}}$

$\frac{I_{1}}{I_{2}}=(\frac{l_{2}}{l_{1}})(\frac{r_{1}}{r_{2}})$

$\frac{I_{1}}{I_{2}}=\left ( \frac{3}{4} \right )\left ( \frac{2}{3} \right )^{2}=\frac{3\times 4}{4\times 9}=\frac{1}{3}$

Option 1)

$3$

This option is incorrect.

Option 2)

$1/3$

This option is correct.

Option 3)

$8/9$

This option is incorrect.

Option 4)

$2$

This option is incorrect.

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