Question

If  'R' is the equivalent resistance of a parallel circuit and \(r_{1}, r_{2}, r_{3}\) are the resistances of individual resistors, what is the relation between \(\mathrm{R}, r_{1}, r_{2}\) and \(r_{3}\)?

Answer 1

The relation is $$\frac{1}{R} = \frac{1}{r_1} + \frac{1}{r_2} + \frac{1}{r_3}$$.

This follows from $$I = I_1 + I_2 + I_3$$ and the fact that the potential difference is the same across every resistor, using Ohm's law.