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