, , and are in parallel, so we add them by using:

We find that

, , and  are in series. So we use:

 We will then determine the total current of the circuit.

Once again, using

Where  is the resistance of the resistor in question, we get

, , and are in parallel, so we add them by using:

We find that

, , and  are in series. So we use:

First, we need to find the total current of the circuit, we simply use:

Because ,  and  are in parallel,

Also, the voltage drop must be the same across all three

Using

Using algebraic subsitution we get:

Solving for

Using

Due to the "loop rule", the voltage increase in the battery will need to be equal to the voltage drop in the resistor.

Use Ohm's law:

Combine equations:

Plug in values:

Due to the "loop rule", the voltage increase in the battery will need to be equal to the voltage drop in the resistor.

Use Ohm's law:

Combine equations:

Plug in values:

In series, resistance adds conventionally.

In series, resistance adds conventionally.

Using Ohm's law for total current:

Now use Ohm's law for an individual resistor:

In series, resistance adds conventionally.

Using

Use Ohm's law:

Converting  to 

First, find the total resistance of the circuit.

 and  are in parallel, so we find their equivalent resistance by using the following formula:

Next, add the series resistors together.

Use Ohm's law to find the current in the system.

The current through  and  needs to add up to the total current, since they are in parallel.

Also, the voltage drop across them need to be equal, since they are in parallel.

Set up a system of equations.

Solve.

In this question, we're shown a circuit diagram with two resistors connected in parallel. We're also told that both resistors have the same resistance. We're then asked to determine how the current through one of the resistors will change if the other one is removed.

To answer this question, we'll need to take Ohm's law into account, which states the following.

Moreover, for two resistors connected in parallel, the equivalent resistance is found by summing the inverses of the individual resistors. In the event that two resistors have the same value, as in this case, the equivalent resistance will be cut in half.

Since the equivalent resistance of the circuit is half as great as either resistor, the removal of  will cause the overall resistance of the circuit to become twice as great. When the resistance becomes twice as great, and voltage does not change, the current through the circuit will become halved.

Now, it's important to realize that the current of the entire circuit becomes half as great. But remember that in the original circuit, the overall current (which was twice as great) was split between the two resistors. Thus, even though the overall current in the circuit is being cut in half, the entirety of the new current is flowing solely through . Therefore, the current flowing through this circuit does not change, even though the current for the entire circuit does.