Question

Find the total resistance in each of the cases:

a) Three 30 Ohm light bulbs and two 20 Ohm heating elements connected in a series.

b) Two strings of Christmas tree lights if the first string has eight 4 Ohm bulbs in series and the second has twelve 3 Ohm bulbs in series.

Answer 1

a) Given quantities:

light bulbs:

$n_1 =3 \space\space\space R_1 = 30\Omega \space \space parallel$

heating elements

$n_2 = 2 \space \space \space R_2 = 20\Omega \space \space parallel$

and light bulbs and heating elements connected in series:

$R = \frac{R_1}{n_1}+\frac{R_2}{n_2}=\frac{30}{3}+\frac{20}{2} = 20\Omega$

b) Given quantities:

first string's lights:

$n_1 = 8 \space \space \space R_1 = 4\Omega \space \space in \space series$

second string's lights:

$n_1 = 12 \space \space \space R_1 = 3\Omega \space \space in \space series$

and first and second strings are connected parallel

$R = \frac{n_1R1*n_2R_2}{n_1R_1+n_2R2}= \frac{8*4*12*3}{32+36} \approx 17 \Omega$