Circuits In Parallel

Question

Two Resistors R1=6Ohms And R2=12Ohms Are Connected In Parallel To Each Other And In Series To R3=2Ohms. What Is The Net Resistance In The Circuit?

Answer 1

First, solve for the parallel combination of R₁ and R₂.

1/R = 1/R₁ + 1/R₂

R = R₁R₂ / (R₁ + R₂)

Next, combine R in series with R₃ and get the equivalent resistance.

R_e = R + R₃ = [R₁R₂ / (R₁ + R₂)] + R₃

Now plug in the values of R₁, R₂, and R₃, and finish from here.

Answer 2

The total from parallel resistors R1 and R2 is

1/R1 + 1/R2 = (R1 + R2) / (R1R2).

The resistance for the R1/R2 pair is the reciprocal of the above (thanks to Arturo for catching this).

R3 is then in series to the above so the total resistance in the circuit is

R3 + (R1 R2)/(R1 + R2)