Question

State the sailent features for parallel combination and series combination of resistor . Derive the formula for effective resistance for three resistance combined in parallel combination

Answer 1

Unlike the previous series resistor circuit, in a parallel resistor network the circuit current can take more than one path as there are multiple paths for the current. Then parallel circuits are classed as current dividers.

Since there are multiple paths for the supply current to flow through, the current may not be the same through all the branches in the parallel network. However, the voltage drop across all of the resistors in a parallel resistive network IS the same. Then, Resistors in Parallel have a Common Voltage across them and this is true for all parallel connected elements.

So we can define a parallel resistive circuit as one where the resistors are connected to the same two points (or nodes) and is identified by the fact that it has more than one current path connected to a common voltage source. Then in our parallel resistor example below the voltage across resistor R1 equals the voltage across resistor R2 which equals the voltage across R3 and which equals the supply voltage. Therefore, for a parallel resistor network this is given as: