4. The total resistance in a parallel circuit is the sum of the reciprocals of the resistances.
[tex]\frac{1}{R_T} =\frac{1}{R_1} +\frac{1}{R_2} ...\\\frac{1}{R_1} = \frac{1}{3} +\frac{1}{5} +\frac{1}{6} \\\frac{1}{R_T} = \frac{7}{10} \\R_T=\frac{10}{7}[/tex]
Therefore, the total resistance is [tex]\frac{10}{7}[/tex] Ω, or approximately 1.43 Ω.
5. The total resistance in a series circuit is the sum of the resistance.
[tex]R_T=R_1+R_2...\\R_T=3+10+5\\R_T=18[/tex]
Therefore, the total resistance is 18 kΩ.
6. a)
[tex]\frac{1}{R_T} = \frac{1}{7}+\frac{1}{5} +\frac{1}{2} \\\frac{1}{R_T} =\frac{59}{70} \\R_T=\frac{70}{59}[/tex]
Therefore, the total resistance is [tex]\frac{70}{59}[/tex] Ω, or approximately 1.19 Ω.
b)
[tex]R_T=R_1+R_2...\\R_T=2+5\\R_T=7[/tex]
Therefore, the total resistance is 7 Ω.
c)
[tex]R_T=R_1+R_2...\\R_T=2+5+7\\R_T=14[/tex]
Therefore, the total resistance is 14 Ω.
I hope this helps!
