Physics, asked by Anzie2478, 10 months ago

two wires of same length and area made of two materials of resistivity rho 1 and rho 2. find equivalent resistivity in a) series and b) parallel.

Answers

Answered by Rahilahmedshaikh111
72

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Answered by muscardinus
24

The equivalent resistivity in (a) series and (b) parallel is as follows :

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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