Question

(a) Find the total resistance of the series parallel circuit shown below looking from the terminal A and B. (5 points) (b) Find the total resistance of the series parallel circuit shown below looking from the terminal A and B. (5 points)

Answer 1

a) Total Resistance from ab terminal = R1 parallel to R4 in series with R3 & R2

R1 parallel R4 = R'

$\frac{1}{R^{'}}=\frac{1}{R_{1}}+\frac{1}{R_{4}}$

   $=\frac{1}{2k}+\frac{1}{2k}$

R' = 1k

R between A-B = R' + R₃ + R₂

= 1 k + 6k + 10k

= 17k

2) Resistance between A & B = R1 parallel R2 + R3 parallel R4

$\frac{1}{R_{12}}=\frac{1}{R_{1}}+\frac{1}{R_{2}}$

$=\frac{1}{2.2k}+\frac{1}{10k}$

R₁₂ = 22k/12.2k = 1.82 k

$\frac{1}{R_{34}}=\frac{1}{R_{3}}+\frac{1}{R_{4}}$

$=\frac{1}{10k}+\frac{1}{2.2k}$

R₃₄ = 22k/12.2

= 18.82k

R between A & B

= R₁₂ +R₃₄

= 1.82k + 1.82k

= 3.64k