Given the expression:
[tex]R=\frac{1}{\frac{1}{R1}+\frac{1}{R2}+\frac{1}{R3}}[/tex]
And:
R1 = 2 ohms;
R2 = 3 ohms;
R3 = 3 ohms.
Substitute the values to find R.
[tex]R=\frac{1}{\frac{1}{2}+\frac{1}{3}+\frac{1}{3}}[/tex]
Take the least common denominator of 2, 3, 3.
The multiples of 2: 2, 4, 6, 8 ...
Multiples of 3: 3, 6, 9 ...
So, the least common denominator is 6. Then,
[tex]\begin{gathered} R=\frac{1}{\frac{3+2+2}{6}} \\ R=\frac{1}{\frac{7}{6}} \end{gathered}[/tex]
To divide 2 fractions, flip the second fraction, then multiply. So,
[tex]\begin{gathered} R=1\cdot\frac{6}{7} \\ R=\frac{6}{7} \end{gathered}[/tex]
Answer: The total resistance is 6/7.
