Answer to Question #282606 in Electric Circuits for Anonymous005

Question

Calculate the total resistance of two, three, four and five 60 Ω resistors in parallel. What is the simple relationship for the total resistance of equal resistances in parallel?

Answer 1

Total resistance of two 60 Ω resistors in parallel

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

$=\frac{1}{60}+\frac{1}{60}$

$=\frac{2}{60}=\frac{1}{30}$

$\frac{1}{R_{T}}=\frac{1}{30}$

${R_{T}}=30Ω$

Total resistance of three 60Ω resistors in parallel

$\frac{1}{R_{T}}=\frac{1}{R_{1}}+\frac{1}{R_{2}}+\frac{1}{R_{3}}$

$=\frac{1}{60}+\frac{1}{60}+\frac{1}{60}$

$=\frac{3}{60}$

$=\frac{1}{20}$

$\frac{1}{R_{T}}=\frac{1}{20}$

${R_{T}}=20Ω$ 

Total resistance of four 60Ω resistors in parallel

$\frac{1}{R_{T}}=\frac{1}{R_{1}}+\frac{1}{R_{2}}+\frac{1}{R_{3}}+\frac{1}{R_{4}}$

$=\frac{1}{60}+\frac{1}{60}+\frac{1}{60}+\frac{1}{60}$

$=\frac{4}{60}$

$\frac{1}{R_{T}}=\frac{1}{15}$

$R_{T}=15Ω$

Total resistance of five 60Ω resistors in parallel

$\frac{1}{R_{T}}=\frac{1}{R_{1}}+\frac{1}{R_{2}}+\frac{1}{R_{3}}+\frac{1}{R_{4}}+\frac{1}{R_{5}}$

$=\frac{1}{60}+\frac{1}{60}+\frac{1}{60}+\frac{1}{60}+\frac{1}{60}$

$=\frac{5}{60}$

$\frac{1}{R_{T}}=\frac{1}{12}$

$R_{T}=12Ω$

The simple relationship for the total resistance of equal resistances in parallel if given a 60Ω resistor is

$R_{T}=\frac{60Ω}{n}$ for $n=2,3,4,...$