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.

To find the current in a circuit with a battery and resistor(s), you use Ohm's Law.

We have the voltage and we have the resistance, so we don't need to rearrange the equation.

Therefore, the current through the resistor is 2 amps ().

The relevant equation for this problem is Ohm's law.

We're given the voltage and the current, so we need to rearrange to get the resistance.

To begin with, we'll need to calculate the current that is flowing through this circuit. We can do this by using Ohm's law.

Now that we have an expression that gives us the current, which is in units of charge per second, we'll need to calculate the moles of charge per second.

This expression directly above gives the total amount of charge that passes within a given time frame. But to find the moles of charge, we'll need to use Faraday's constant.

First, we need to find the total resistance of the circuit. In order to find the total resistance of the circuit, we need to combine all of the parallel resistors first, then add them together as resistors in series.

Combine  with :

Combine  with :

Combine  with :

Then, add the combined resistors, which are now all in series: 

Then, we will need to use Ohms law to determine the total current of the circuit

Combine all of our voltage sources: 

Plug in our values:

We know that the voltage drop across parallel resistors must be the same, so:

Use Ohm's law:

We also know that:

Substitute:

Solve for :

First, we need to find the total resistance of the circuit. In order to find the total resistance of the circuit, we need to combine all of the parallel resistors first, then add them together as resistors in series.

Combine  with :

Combine  with :

Combine  with :

Then, add the combined resistors, which are now all in series: 

Then, we will need to use Ohm's law to determine the total current of the circuit: 

Combine all of our voltage sources: 

Plug in our values:

We know that the voltage drop across parallel resistors must be the same, so:

Use Ohm's law:

We also know that:

Substitute: 

Solving for :

We plug in our values:

First, we need to find the total resistance of the circuit. In order to find the total resistance of the circuit, we need to combine all of the parallel resistors first, then add them together as resistors in series.

Combine  with :

Combine  with :

Combine  with :

Then, add the combined resistors, which are now all in series: 

Then, we will need to use Ohms law to determine the total current of the circuit.

Combine all of our voltage sources: 

Plug in our values:

We know that the voltage drop across parallel resistors must be the same, so:

Use Ohm's law:

We also know that:

Substitute: 

Solve for :

Plug in our values:

First, we need to find the total resistance of the circuit. In order to find the total resistance of the circuit, we need to combine all of the parallel resistors first, then add them together as resistors in series.

Combine  with :

Combine  with :

Combine  with :

Then, add the combined resistors, which are now all in series: 

Then, we will need to use Ohm's law to determine the total current of the circuit.

Combine all of our voltage sources:

Plugin our values:

We know that the voltage drop across parallel resistors must be the same, so:

Use Ohm's law:

We also know that:

Substitute: 

Solving for :

Plug in our values: