Question

An equilateral triangle with each side having resistance of 2 ohm. What is the effective resistance across any side

Answer 1

Answer:

4/3ohm

Explanation:

1/R=1/4+1/2

1/R= 1+2/4

1/R=3/4

R=4/3

Answer 2

Answer:

The effective resistance across any side is $\frac{4}{3}\Omega$.

Explanation:

We will solve this question by the series and parallel combination of resistors.

Here there is an equilateral triangle ABC  each having the resistance of 2Ω.

We have to find effective resistance across any side of the triangle. So, we choose the side AC across which we will find the effective resistance.

The sides AB and BC are in series and this, in turn, is parallel with the side AC.

The series resistance of side AB and BC is given as R₁ i.e.

$R_1=R_A_B+R_B_C$            (1)

$R_1=2\Omega+2\Omega=4\Omega$        (2)

And effective resistance will be given as,

$\frac{1}{R_e_f_f}=\frac{1}{R_1}+\frac{1}{R_A_C}$            (3)

As R₁ and AC are parallel,

By putting the value of R₁ and AC in equation (3) we get;

$\frac{1}{R_e_f_f}=\frac{1}{4}+\frac{1}{2}$

$R_e_f_f=\frac{4}{3}\Omega$

Hence, the effective resistance across any side is $\frac{4}{3}\Omega$.