Question

Why does resistance decrease when resistors are added in parallel?

Answer 1

Let's say that we have two resistors of ldngth `L` and resistivity `rho`, `a` and `b`. Resistor `a` has a cross-sectional surface area `A` and resistor `b` has a cross-sectional surface area `B`. We say that when they are in parallel, they have a combined cross-sectional surface area of `A+B`.

Resistance can be defined by:
`R=(rhol)/A`, where:

• `R` = resistance (`Omega`)
• `rho` = resistivity (`Omegam`)
• `l` = length (`m`)
• `A` = cross-sectional surface area (`m^2`)

`R_A=(rhol)/a`
`R_B=(rhol)/b`
`R_text(total)=(rhol)/(a+b)`

Siince for `A` and `B`, `rho` and `l` are constant:
`R_text(total)propto1/A_text(tofal)`

As the cross-sectional surface area increases, resistance decreases.

In terms of particle motion, this stands true, since the electrons have two paths to take, and combined, they have more space to flow through.