First slide

Resistivity of various materials

Question

Two uniform wires A and B are of the same metal and have equal masses. The radius of wire A is thrice that of wire B . The total resistance of A and B when connected in parallel is

Easy

A

$4.20 Ω$ when the resistance of wire A is $4 .25 Ω$
B

$5 Ω$ when the resistance of wire A is $4 .25 Ω$
C

$4 Ω$ when the resistance of wire B is $4 .25 Ω$
D

$4 Ω$ when the resistance of wire B is $4 .25 Ω$

Solution

$\frac{R_{A}}{R_{B}} = {(\frac{r_{B}}{r_{A}})}^{4} \Rightarrow \frac{R_{A}}{R_{B}} = {(\frac{1}{3})}^{4} = \frac{1}{81} \Rightarrow R_{B} = 81 R_{A}$
When RA and RB are connected in parallel then equivalent resistance
$R_{eq} = \frac{R_{A} R_{B}}{(R_{A} + R_{B})} = \frac{81}{82} R_{A}$
If $R_{A} = 4 .25 Ω then R_{eq} = 4 .20 Ω$ i.e. option (a) is correct.

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