First slide

combination of resistance

Question

A uniform wire of resistance 36 ohm is bent in the form of a circle as shown in fig The effective resistance across the points A and B is

Moderate

A

5 $Ω$
B

6 $Ω$
C

7.2 $Ω$
D

30 $Ω$

Solution

Let r be the resistance of total length of circular wire' The resistance of smaller arc $AB, r_{1} = r / 6 = 36 / 6 = 6 Ω$ The resistance of bigger arc
$r_{2} = 5 r / 6 = (5 \times 36) / 6 = 30 Ω$ Resistances r₁ and r₂ are in parallel between points A and B, Therefore,
$\begin{aligned} \frac{1}{R} = \frac{1}{r_{1}} + \frac{1}{r_{2}} = \frac{1}{6} + \frac{1}{30} = \frac{6}{30} = \frac{1}{5} \\ ∴ R = 5 Ω \end{aligned}$

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