Question

Three resistors each of 5 ohms are connected in the form of a triangle. What is the resistance between the vertices?

(a) \(\frac {3}{10}\)

(b) \(\frac {10}{3}\)

(c) \(\frac {15}{50}\)

(d) \(\frac {2}{5}\)

I had been asked this question by my school teacher while I was bunking the class.

My question is taken from Combination of Resistors in portion Current Electricity of Physics – Class 12

Answer 1

The correct choice is (b) \(\frac {10}{3}\)

Easy explanation: Equivalent resistance = 5 + 5 + \(\frac {1}{5}\) (since first two are in series, and they are in parallel to the third in case of a triangular arrangement)

 \(\frac {1}{R}\) = 10 + \(\frac {1}{5} = \frac {(5 + 10)}{5 \times 10} = \frac {15}{50} = \frac {3}{10}\)

Thus, R = \(\frac {1}{\frac {3}{10}} = \frac {10}{3}\) ohms

Therefore, the equivalent resistance is \(\frac {10}{3}\) ohms.