Question

A wire of length 10 cm and resistance 12 ohms is bent to form a full circle. What is the effective resistance between two diametrically opposite points of the circle?

Answer 1

Answer:

2.5

Explanation:

two parts having resistance 5 each will be in parallel

Answer 2

Answer:

The effective resistance between two diametrically opposite points of the circle is 0.3Ω.

Explanation:

The total resistance of the wire is calculated as,

$\mathrm{R_T=R\times l}$          (1)

Where,

$\mathrm{R_T}$=total resistance of the wire

R=initial resistance of the wire

l=length of the wire

From the question we have,

The length of the wire(l)=10 cm=10×10⁻²m

The initial resistance of the wire(R)=12Ω

We obtain by entering the numbers in equation (1);

$\mathrm{R_T=12\times 10\times 10^{-2}}$

$\mathrm{R_T=1.2\ \Omega}$       (2)

And the resistance of each half(R'),

$\mathrm{R'=\frac{R_T}{2}=\frac{1.2}{2}=0.6\ \Omega}$        (3)

As for diameter, both parts are in parallel so, the equivalent resistance will be,

$\mathrm{R_{eqv}=\frac{R'}{2}=\frac{0.6}{2}=0.3\ \Omega }$      (4)

Hence, the effective resistance between two diametrically opposite points of the circle is 0.3Ω.

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