First slide

Temperature dependence

Question

Two cylindrical conductor having same cross-sectional area ‘A’ and but lengths ‘l’ and ‘2l’ are connected in series combination. Temperature coefficient of resistivities of their materials are $α a n d 2 α$ respectively. Then effective temperature coefficient of resistivity of the combination is

Moderate

A

$\frac{7 α}{3}$
B

$\frac{4 α}{3}$
C

$\frac{5 α}{3}$
D

$\frac{2 α}{3}$

Solution

(3)
$R_{e} = R_{1} + R_{2} = α \frac{l}{A} + 2 α . \frac{2 l}{A} = \frac{5 α l}{A}$
$A s s u m i n g, R_{e} = α_{e} . \frac{l_{e}}{A} = α_{e} . \frac{3 l}{A}$
$α_{e} \frac{3 l}{A} = \frac{5 α l}{A}$
$α_{e} = \frac{5 σ}{3}$

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