Question

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.

Answer 1

Answer:

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Answer 2

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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