First slide

combination of resistance

Question

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

Moderate

A

4Ω when the resistance of wire A is 4.25Ω
B

5Ω when the resistance of wire A is 4.25Ω
C

4Ω when the resistance of wire B is 4.25Ω
D

4Ω when the resistance of wire B is 4.25Ω

Solution

$\frac{R_{A}}{R_{B}} = {(\frac{r_{B}}{r_{A}})}^{4} \Rightarrow \frac{R_{A}}{R_{B}} = {(\frac{1}{2})}^{4} = \frac{1}{16} \Rightarrow R_{B} = 16 R_{A}$
When R_A and R_B are connected in parallel then equivalent resistance
$R_{eq} = \frac{R_{A} R_{B}}{(R_{A} + R_{B})} = \frac{16}{17} R_{4}$
If $R_{A} = 4 .25 Ω$ then $R_{eq} = 4 Ω$ i.e. option (a) is correct.

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