A straight uniform wire of resistance 36 Omeg | vedclass

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Question

(A) The total resistance of the wire is $R = 36 \Omega$.
When the wire is bent into a semi-circular loop,the wire is divided into two equal halves al

Vedclass · Accepted Answer

$9 \Omega$

Vedclass · Answer

(A) The total resistance of the wire is $R = 36 \Omega$.
When the wire is bent into a semi-circular loop,the wire is divided into two equal halves along the diameter.
Each half has a resistance of $R' = \frac{R}{2} = \frac{36}{2} = 18 \Omega$.
These two halves are connected in parallel between the ends of the diameter.
The equivalent resistance $R_{eq}$ is given by the formula for parallel resistors: $\frac{1}{R_{eq}} = \frac{1}{R'} + \frac{1}{R'}$.
$\frac{1}{R_{eq}} = \frac{1}{18} + \frac{1}{18} = \frac{2}{18} = \frac{1}{9}$.
Therefore,$R_{eq} = 9 \Omega$.

$A$ straight uniform wire of resistance $36 \Omega$ is bent in the form of a semi-circular loop. The effective resistance between the ends of the diameter of the semi-circular loop is

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