Question

Find the equivalent resistance from the indicated terminal pair of the networks in the attached doc

Answer 1

a) R = 2.5 Ω, b) R = 1 Ω, c) R = 2R / 3 Ω

Step-by-step explanation:

The resistance configuration can be in series or in parallel, for each one the equivalent resistance can be calculated

series, the equivalent resistance is the sum of the resistances

parallel, the inverse of the equivalent resistance is the inverse of the sum of the resistances

let's apply these principles to each case

case a)

equivalent series resistance

R₁ = 1 +4 = 5 ohm

R₂ = 2 +3 = 5 ohn

these two are in parallel

1 / R = 1/5 +1/5

1 / R = 2/5

R = 2.5 Ω

case B

we solve the parallel

1 / R₁ = ½ + ½ = 1

R₁ = 1 Ω

we solve the resistors in series

R₂ = 1 + 1

R₂ = 2 Ω

finally we solve the last parallel

1 / R = ½ +1/2 = 1

R = 1 Ω

case C

we solve house resistance pair in series

R₁ = R + 2R = 3R

we go to the next mesh

R₂ = R + 2R = 3R

R₃ = R + 2R = 3R

last mesh

R₄ = R + R = 2R

now we solve the parallel of this equivalent resistance

1 / R = 1 / R₁ + 1 / R₂ + 1 / R₃ + 1 / R₄

1 / R = 1 / 3R + 1 / 3R + 1 / 3R + 1 / 2R

1 / R = 3 / 3R + 1 / 2R = 1 / R + 1 / 2R

1 / R = 3 / 2R

R = 2R / 3 Ω