Question

Find the total resistance of three resistors in parallel if their individual resistance are...

Answer 1

Given the expression:

`R=(1)/((1)/(R1)+(1)/(R2)+(1)/(R3))`

And:

R1 = 2 ohms;

R2 = 3 ohms;

R3 = 3 ohms.

Substitute the values to find R.

`R=(1)/((1)/(2)+(1)/(3)+(1)/(3))`

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,

`\begin{gathered} R=(1)/((3+2+2)/(6)) \\ R=(1)/((7)/(6)) \end{gathered}`

To divide 2 fractions, flip the second fraction, then multiply. So,

`\begin{gathered} R=1\cdot(6)/(7) \\ R=(6)/(7) \end{gathered}`

Answer: The total resistance is 6/7.