Question 163: Current Electricity

Question

Two wires of same length and thickness having specific resistances 6$\Omega$ cm and 3$\Omega$ cm respectively are connected in parallel. The effective resistivity is $\rho$$\Omega$ cm. The value of $\rho$, to the nearest integer, is ____________.

Accepted Answer

Let length of each wire is l and area A. When they are connected in parallel then their effective area 2A.
From formula we know,
${R_{eq}} = {{{R_1}{R_2}} \over {{R_1} + {R_2}}}$
$ \Rightarrow {{ho l} \over {2A}} = {{{ho _1}{l \over A} 	imes {ho _2}{l \over A}} \over {{ho _1}{l \over A} + {ho _2}{l \over A}}}$
$ \Rightarrow {ho  \over 2} = {{{ho _1} 	imes {ho _2}} \over {{ho _1} + {ho _2}}}$
$ \Rightarrow {ho  \over 2} = {{6 	imes 3} \over {6 + 3}} = 2$
$ \Rightarrow ho  = 4$

Current Electricity

Two wires of same length and thickness having specific resistances 6\Omega cm and 3\Omega cm respectively are connected in parallel. The effective resistivity is \rho\Omega cm. The value of \rho, to the nearest integer, is ____________.

Integer / Numeric Answer Type