Question

You have three resistors in a parallel circuit with resistances 6 ohms, 12 ohms, and 24 ohms. What is the total resistance of the circuit?

Answer 1

$$
\Large \frac{1}{R_{total}} =\frac{1}{R_{1}} + \frac{1}{R_{2}} +\frac{1}{R_{3}} $$

Answer 2

so you can plug that in

Answer 3

I did that, I plugged in 6, 12, and 24, but didn't know really what to do next

Answer 4

$$\LARGE R_{total} =\frac{1}{\frac{1}{R_{1}} + \frac{1}{R_{2}} +\frac{1}{R_{3}}}$$

Answer 5

but the answer is 24/7 and I have no idea how that worked out

Answer 6

$$\LARGE R_{total} =\frac{1}{\frac{1}{6} + \frac{1}{12} +\frac{1}{24}}\\

\LARGE=\frac{1}{\frac{4}{24} + \frac{2}{24} +\frac{1}{24}}\\

\LARGE =\frac{1}{\frac{(4+2+1)}{24}} =\frac{1}{\frac{7}{24}} =

\frac{24}{7} \\

$$

Answer 7

$$\LARGE R_{total} =\frac{1}{\frac{1}{6} + \frac{1}{12} +\frac{1}{24}} \\[0.5 in]
\text{use common denominator}\\[0.1in]

\LARGE=\frac{1}{\frac{4}{24} + \frac{2}{24} +\frac{1}{24}}\\[0.1 in]

\LARGE =\frac{1}{\frac{(4+2+1)}{24}} =\frac{1}{\frac{7}{24}} =

\frac{24}{7} \\

$$