An electric current is passed through a circuit containing two wires of same material, connected in parallel. If the lengths and radii of the wires are in the ratio of 3:2 and 2:3, then the ratio of the current passing through the wire will be
(i) 2:3
(ii) 3:2
(iii) 8:27
(iv) 27:8
(iii) 8:27
Explanation:
`"l"_{1}` : `"l"_{2}` = 3:2
`"r"_{1}` : `"r"_{2}` = 2:3
`"I"_{1}` : `"I"_{2}` = ?
`"R"_{1}` = ρ`\frac{l_{1}}{\pi r_1^{2}}`
`"R"_{2}` = ρ`\frac{l_{1}}{\pi r_2^{2}}`
`\frac{R_{1}}{R_{2}}`=`\frac{l_{1}}{l_{2}}``\frac{\pi r_2^{2}}{\pi r_2^{2}}` =`\frac{l_{1}}{l_{2}}``\times``\frac{r_2^{2}}{r_2^{2}}`
`\frac{3}{2}\times(\frac{3}{2})^{2}=\frac{3^{3}}{2^{3}}=\frac{27}{8}`
`\frac{"I"_{1}}{"I"_{2}}=\frac{"V/R"_{1}}{"V/R"_{2}}`
`\frac{"R"_{2}}{"R"_{1}}=\frac{8}{27}`
0 Comments