Question

16. A wire of resistance 12 ohms per meter is bent to form a complete circle of radius 10 cm. The
resistance between its two diametrically opposite points, A and B as shown in the figure, is :
(A) 60
(B) 0.60
(C)302
(D) 602
​

Answer 1

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Answer 2

Answer:

0.6π Ω

B is correct

Explanation:

Given that,

Radius = 10 cm

Resistance = 12 ohm

Firstly, we need to calculate the length of the wire

$L=2\pi\times r$

Put the value into the formula

$L=2\pi\times0.1$

$L=0.2\pi\ m$

We need to calculate the resistance between its two diametrically opposite points,

The wire divided into two parts point A and B.

Resistance of each part is equal.

$R_1=R_2=\dfrac{0.2\pi\times12}{2}$

$R=1.2\pi\ \Omega$

Both parts are connected in parallel and resultant resistance is R

$\dfrac{1}{R}=\dfrac{1}{R_1}+\dfrac{1}{R_2}$

$\dfrac{1}{R}=\dfrac{1}{1.2\pi}+\dfrac{1}{1.2\pi}$

$R=0.6\pi\ \Omega$

Hence, The resistance between points A and B is 0.6π Ω