Another conductor with resistance R was connected in series with another of the same material, of the same length

Another conductor with resistance R was connected in series with another of the same material, of the same length, but with a cross-sectional area that is half that. What will be their total resistance.

1. When the conductors are connected in series, their total resistance is equal to their sum.
Rtot = R + R1
2. Let’s write down the expression to determine the resistivity of the wire:
ρsp = R * Ssech / l, where R is the resistance of the wire, l is the length of the wire, Ssech is the cross-sectional area.
3. Let us express R from here:
R = ρsp * l / Ssection
For the first conductor with resistance R we have:
R = ρsp * l / Ssech1
For the second conductor with resistance R1 we have:
R1 = ρsp * l / Ssec2
4. We have on condition:
Ssech1 / Ssech2 = 2
Divide R1 / R
R1 / R = (ρsp * l / Ssech2) / (ρsp * l / Ssec1) = Ssec1 / Ssec2 = 2
Find from this expression R1:
R1 = 2R
5. Determine the total resistance:
Rtot = R + R1 = R + 2R = 3R
Answer: the total resistance will be Rtot = 3R