Question:
Two wires of same length and thickness having specific resistances $6 \Omega \mathrm{cm}$ and $3 \Omega \mathrm{cm}$ respectively are connected in parallel. The effective resistivity is $\rho \Omega \mathrm{cm}$. The value of $\rho$ to the nearest integer, is
Solution:
(4)
$\because$ in parallel
$\mathrm{R}_{\mathrm{net}}=\frac{\mathrm{R}_{1} \mathrm{R}_{2}}{\mathrm{R}_{1}+\mathrm{R}_{2}}$
$\frac{\rho \ell}{2 \mathrm{~A}}=\frac{\rho_{1} \frac{\ell}{\mathrm{A}} \times \rho_{2} \frac{\ell}{\mathrm{A}}}{\rho_{1} \frac{\ell}{\mathrm{A}}+\rho_{2} \frac{\ell}{\mathrm{A}}}$
$\frac{\rho}{2}=\frac{6 \times 3}{6+3}=2$
$\rho=4$
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