Question

If a resister of resistance R is cut 3 equal parts.then what is the resistance of equivalent r when connected in parallel?

Answer 1

`R/9`

Explanation:

For the resistor: `R = (rho l)/A`

For constant `rho, A`, then `R propto l`

So if you cut a resistor `R` into 3 parts length-wise , you have 3 resistors of resistance `tildeR` where:

• `tildeR = R/3`

Their combined resistance in parallel is then:

`1/tildeR_c = 1/( R/3) + 1/( R/3) + 1/( R/3) = 3 *1/( R/3) = 9/ R`

`implies tildeR_c = R/9`