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$$\Omega$ cm. The value of $\rho$, to the nearest integer, is ____________.
Answer (integer)
4
Solution
Let length of each wire is l and area A. When they are connected in parallel then their effective area 2A.<br><br>From formula we know,<br><br>${R_{eq}} = {{{R_1}{R_2}} \over {{R_1} + {R_2}}}$<br><br>$$ \Rightarrow {{\rho l} \over {2A}} = {{{\rho _1}{l \over A} \times {\rho _2}{l \over A}} \over {{\rho _1}{l \over A} + {\rho _2}{l \over A}}}$$<br><br>$$ \Rightarrow {\rho \over 2} = {{{\rho _1} \times {\rho _2}} \over {{\rho _1} + {\rho _2}}}$$<br><br>$\Rightarrow {\rho \over 2} = {{6 \times 3} \over {6 + 3}} = 2$<br><br>$\Rightarrow \rho = 4$
About this question
Subject: Physics · Chapter: Current Electricity · Topic: Ohm's Law and Resistance
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