Question

An equilateral triangle has constructed with a uniform wire whose resistance per unit lenth is 4ohm/cm if the length of each side of triangle is 10 cm the resistance across any side

Answer 1

Answer: 26.67 Ω

Explanation:

Step 1:

A uniform wire has being constructed into an equilateral triangle ABC as shown in figure 1.

Length of each side of the triangle = 10 cm

The resistance of the wire per cm = 4 Ω

∴ The resistance of the wire of length 40 cm = 10 * 4 = 40 Ω per branch of the equilateral triangle ABC

Step 2:

From figure 1., we can see the resistance across branches AB and AC are connected in series.

So, by applying the formula of series combination of resistance, we get

The resistance = R(AB) + R(AC) = 40+40 = 80 Ω

Step 3:

Now, from figure 3., we can see that the resistance of 80 ohms and the resistance across branch BC is connected in parallel.

So, by applying the formula of parallel combination of resistance, we get (as shown in figure 3.)

The net resistance, 1/R

= (1/80) + [1/R(BC)]

= 1/80 + 1/40

= (1+2)/80

= 3/80

= 26.67 Ω

Thus, the net resistance across any side is 26.67 ohms.