Question

How is resistance affected as more branches are added to a parallel circuit?

Answer 1

The total resistance decreases

Step-by-step explanation:

The total resistance of a parallel circuit is given by:

`(1)/(R_T)=(1)/(R_1)+(1)/(R_2)+...`

where R1, R2, etc. are the individual resistances.

We notice that if we add one more resistor in parallel, we add another positive term
`(1)/(R)` to the sum, therefore the term
`(1)/(R_T)` increases. However, this term is the reciprocal of the total resistance: therefore, this means that the total resistance will decrease.