Two wires of same length and area made up of two material of resistivity rho 1and rho2 are connected in parallel V to a source of potential the equivalent resistivity of same length and area?
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Explanation:
Two wires of same length and area made of two materials of resistivity \rho_1\ and\ \rho_2. The equivalent resistance of resistors in series combination is given by :
R_{eq}=R_1+R_2
Since,
R=\rho\dfrac{l}{A} ...........(1)
Where
length and area of two materials are same
\dfrac{\rho_{eq}l}{A}=\dfrac{\rho_1l}{A}+\dfrac{\rho_2l}{A}
So,
\rho_{eq}=\rho_1+\rho_2
The equivalent resistance of resistors in parallel combination is given by :
\dfrac{1}{R_{eq}}=\dfrac{1}{R_1}+\dfrac{1}{R_2}
Using equation (1) we get :
\dfrac{A}{\rho_{eq} l}=\dfrac{A}{\rho_1 l}+\dfrac{A}{\rho_2 l}
So,
\dfrac{1}{\rho_{eq}}=\dfrac{1}{\rho_1}+\dfrac{1}{\rho_2}
Hence, this is the required solution.
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Resistivity
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