A conductor of resistance 3 $Ω$ is stretched uniformly till its length is doubled. The wire now is bent in the form of an equilateral triangle. The effective resistance between the ends of any side of the triangle in ohms is :

\frac{9}{2}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

\frac{8}{3}

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

2

No worries! We‘ve got your back. Try BYJU‘S free classes today!

1

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is B $\frac{8}{3}$
$V_{1} = V_{2}$
$L_{1} A_{1} = L_{2} A_{2}$
$\frac{L_{1}}{A_{1}} = \frac{L_{2}}{A_{2}}$

$\Rightarrow \frac{A_{1}}{A_{2}} = \frac{2}{1}$

$\frac{R_{1}}{R_{2}} = (\frac{L_{1}}{L_{2}}) (\frac{A_{2}}{A_{1}})$
$\frac{R_{1}}{R_{2}} = \frac{1}{2} \times \frac{1}{2}$

$R_{2} = 4 R_{1} = 12 Ω$

$R_{A B} = \frac{2 R_{2}}{9} = \frac{2}{3} \times 4$

$R_{A B} = \frac{8}{3} Ω$

Suggest Corrections

Similar questions

Q. A conductor of resistance

3 Ω

is stretched uniformly till its length is doubled. The wire is now bent in the form of an equilateral triangle. The effective resistance between the ends of any side of the triangle in

Ω

A wire has a resistance of 6 ohms. It is bent in the form of an equilateral triangle. The effective resistance between any two corners of the triangle is

Q. A wire of length l is bent into the form of an equilateral triangle. The effective resistance between any two vertices of the triangle is 'R'. If the same wire is bent into the form a square, what will be the effective resistance between the ends of one side?

Q. A wire of resistance

18

ohm is bent to form an equilateral triangle. The resistance across any two vertices of the triangle is (in ohm):

Q. A wire having resistance

12 Ω

is bent in the form of an equilateral triangle. The effective resistance between any two corners of the triangle will be

Join BYJU'S Learning Program

A conductor of resistance 3Ω is stretched uniformly till its length is doubled. The wire now is bent in the form of an equilateral triangle. The effective resistance between the ends of any side of the triangle in ohms is :

The correct option is B 83V1=V2L1A1=L2A2L1A1=L2A2⇒A1A2=21R1R2=(L1L2)(A2A1)R1R2=12×12R2=4R1=12ΩRAB=2R29=23×4RAB=83Ω

A conductor of resistance 3 $Ω$ is stretched uniformly till its length is doubled. The wire now is bent in the form of an equilateral triangle. The effective resistance between the ends of any side of the triangle in ohms is :