Hi there! :)
Reference the diagram below for clarification.
1.
We must begin by knowing the following rules for resistors in series and parallel.
In series:
[tex]R_T = R_1 + R_2 + ... + R_n[/tex]
In parallel:
[tex]\frac{1}{R_T} = \frac{1}{R_1} + \frac{1}{R_2} + ... + \frac{1}{R_n}[/tex]
We can begin solving for the equivalent resistance of the two resistors in parallel using the parallel rules.
[tex]\frac{1}{R_{T, parallel}} = \frac{1}{10} + \frac{1}{10}\\\\\frac{1}{R_{T, parallel}} = \frac{2}{10} = \frac{1}{5}\\\\R_{T, parallel} = 5\Omega[/tex]
Now that we have reduced the parallel resistors to a 'single' resistor, we can add their equivalent resistance with the other resistor in parallel (15 Ohm) using series rules:
[tex]R_T = 15 + 5\\\\\boxed{R_T = 20 \Omega}[/tex]
2.
We can use Ohm's law to solve for the current in the circuit.
[tex]i = \frac{V}{R_T}\\\\i = \frac{120}{20} = \boxed{6 A}[/tex]
3.
For resistors in series, both resistors receive the SAME current.
Therefore, the 15Ω resistor receives 6A, and the parallel COMBO (not each individual resistor, but the 5Ω equivalent when combined) receives 6A.
In this instance, since both of the resistors in parallel are equal, the current is SPLIT EQUALLY between the two. (Current in parallel ADDS UP). Therefore, an even split between 2 resistors of 6 A is 3A for each 10Ω resistor.
4.
Since the 15.0 Ω resistor receives 6A, we can use Ohm's Law to solve for voltage.
[tex]V = iR\\\\V = (6)(15) = \boxed{90 V}[/tex]
