Question

Find the total resistance in each case:

a. A 16 Ω and an 18 Ω resistor connected in parallel

b. A 20 Ω, 10 Ω and 5 Ω resistor connected in parallel

Answer 1

Solution;

For resistors in parallel;

$\frac{1}{R_T}=\frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_3}+...+\frac{1}{R_n}$

(a)

$\frac{1}{R_T}=\frac{1}{16}+\frac{1}{18}=\frac{17}{144}$

Therefore;

$R_T=\frac{144}{17}=8.471\Omega$

(b)

$\frac{1}{R_T}=\frac{1}{20}+\frac{1}{10}+\frac{1}{5}=\frac{7}{20}$

Hence;

$R_T=2.857\Omega$