Physics (resistance)

Question

Two identical resistors connected in series have an equivalent resistance of 8 ohms. The same two resistors, when connected in parallel, will have an equivalent resistance of..

Answer 1

Series Req = R+R = 2R or 8 ohms = 2R, R = 4 ohms

Parallel 1/Req = 1/R + 1/R solve for Reff.

If you have n resistors, R, in series, Req = nR

If you have n resistors, R, in parallel, Req = R/n

which leads to quick answers when resistors are the same.

Answer 2

As the resistances are equivalent, they must each be 4 ohms to have a series equivalent resistance of 8 ohms.

The formula for parallel resistance is 1/R_equiv = 1/ R₁ + 1/R₂ = 1/4 + 1/4 = 1/2.

R_equiv = 2 ohms when connected in parallel.