What is the total current flow through a 120V circuit with one 10-ohm resistor in series with two 10-ohm resistors in parallel?

To understand the solution to this question, we need to analyze the circuit configuration. We have one 10-ohm resistor in series with a combination of two 10-ohm resistors connected in parallel.

First, let's handle the two resistors that are in parallel. The formula for the equivalent resistance ( R_{parallel} ) for resistors in parallel is given by:

[

\frac{1}{R_{parallel}} = \frac{1}{R_1} + \frac{1}{R_2}

]

In this case, both resistors have a value of 10 ohms:

[

\frac{1}{R_{parallel}} = \frac{1}{10} + \frac{1}{10} = \frac{2}{10} = \frac{1}{5}

]

So, the equivalent resistance for the parallel resistors is:

[

R_{parallel} = 5 \text{ ohms}

]

Now, we add this equivalent resistance to the series resistor. The total resistance ( R_{total} ) in the circuit is:

[

R_{total} = R_{series} + R_{parallel} = 10 + 5 =