To find our answer, we have to know how each of the new additions changes the circuit. The addition of the two resistors in series do not affect the current because current is equivalent for resistors in series. However, since there is a resistor in parallel with equivalent resistance to the sum of the 3 resistors in series, current will split evenly amongst the two pathways, thus leading to a current of  flowing through the original resistor. 

In order to find the voltage drop  across , we will use Ohm's law: 

.

However, we first need to solve for the current  in the circuit. This will be calculated by applying Ohm's law to the entire circuit, using the total resistance  for resistors in series. 

Finally, we use this calculated current to find the voltage drop across .

In circuits with resistors, the only thing necessary to determine voltage drop across a resistor is the current through it and the resistance, as given by Ohm's law. 

The first step is to find the equivalent resistance of the entire circuit. Note that R2 and R3 are in parallel, and they are in series with R1. Therefore, in order to find the equivalent resistance:

Then, in order to find the total current, use Ohm's Law:

That means that  will pass through R1, and will split when it reaches the junction between R2 and R3 based on the ratio of the two resistance:

 of current passes through the resistor R3.

The correct answer is Wire B with  and  of current.

The formula for voltage, current and resistance is as follows:

Thus, the wire with the lowest ratio of voltage to current will have the least resistance.

To find the current we must first find the equivalent resistance. For resistors in series, the equivalent resistance is 

For this problem

Now we use Ohm's law, , to find the current, 

To find the current we must first find the equivalent resistance. For resistors in parallel, the equivalent resistance is 

For this problem

Now we use Ohm's law, , to find the current, 

To find the current we must first find the equivalent resistance. This problem is a combination of resistors in series and parallel. First we find the equivalent resistance of resistors in series.

For resistors in series, the equivalent resistance is:

For this problem

The resistors in series can be treated as one  resistor. Now we address the resistors in parallel. For resistors in parallel, the equivalent resistance is:

For this problem

Now we use Ohm's law, , to find the current, 

We know the voltage and total current of the circuit, so we can calculate an equivalent resistance using Ohm's law:

Now we can use the expression for condensing parallel resistors to calculate R3:

The equation for resistance is given by .

From this equation, we can see the best way to decrease resistance is by increasing the cross-sectional area, , of the cord. Increasing the length, , of the cord or the resistivity, , will increase the resistance.