Question

Using Kirchoff's laws and Ohm's law, derive the formula for adding resistors in parallel. You will want to include a diagram and plenty of sentences (not just equations).

Answer 1

Two or more resistor are said to be connected in parallel if the same potential difference exists acorss all the resistors

To find the equivalnet resistance of the combination let us apply a potential difference V between the points P and N, if the current though P is i then

eq-1

The current is divided at the junction P

thus

eq-1

The potential difference across each resistor is

Using ohms law for the resistance R₁, R₂ and R₃ seprately we get

by putting this value in eq-2 we get

or

using eq-1 we get

The process may be generalised for any number of resistors thus