Question

A resistance wire of resistance 18ohm was bent to into an equilateral triangle. Find the resistance between two of its vertices?

Answer 1

ANSWER IS-:  4 Ohms

The resistance given is 18 Ohm,

If the wire is bent in form of equilateral triangle then each sides resistance would become 18/3 Ohm = 6 Ohm..

We have to find resistance across two of its vertices, so we would get a case like, two of its sides are connected in series and both of them would be in parallel with the third side.

So to find equivalent resistance we will first add the resistance of sides in series connection.

So the resistance of those two sides would be like R(s) = R1 + R2

R(s)= 6+6 = 12 Ohms

Now this resistance is in parallel with another 6 Ohm resistance.

So resistance in parallel connection is like,

1/R(p) = 1/R1 + 1/R2

1/R(p) = 1/12 + 1/6

1/R(p) = (1+2)/12

1/R(p) = 3/12

R(p) = 12/3 = 4 Ohms

So our final answer would be 4 Ohms.

Please verify the calculations once again, as I am not good at calculation.

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