# AP Physics 2 : Circuit Power

## Example Questions

### Example Question #1 : Circuit Power

Consider the circuit:

What is the rate of power consumption in the circuit if every resistor has a resistance of ?

Explanation:

To calculate the power consumption of the circuit, we need to first reduce it to an equivalent circuit with a single resistor. Since each resistor has the same resistance, this solution will keep resistance calculations as multiples of  until the circuit is fully reduced.

Start with the two branches in parallel. We can condense R3 and R4, then solve for the total resistance of R2, R3, and R4.

The equivalent circuit now has three resistors in series (R1, Req, and R5), so we can simply add them all up:

Plug in the value for R:

Now we can use the equation for power:

Substituting in Ohm's law for current, we get:

### Example Question #2 : Circuit Power

You have 4 resistors, , , , and , set up like this:

Their resistance are as follows:

If the battery has 8V, what is the total power dissipated through the resistors?

Explanation:

The equation for power is

In order to get the power, we need the current. To find the current, we need to get the total resistance, and use Ohm's Law ().

To find the total resistance, remember the equations for adding resistors is this:

Resistors  and  are in series, resistors  and  are in parallel, and resistors  and  are in series.

Now, we can find the current.

Finally, we can find the power.

Therefore, the power is 16W (watts).

### Example Question #71 : Circuits

Calculate the power consumed across resistor .

Explanation:

To calculate power, we need two of the following three quantities: voltage, current, and resistance.

In this case, since we are lacking the voltage, let's try to find the current.

We can use Kirchoff's junction law to calculate current .

The current coming into the junction = the current coming out of the junction.

Let's take a look at the central junction to the right of resistor .

Now that we know  and , we can calculate power across the resistor.

### Example Question #4 : Circuit Power

Elements A-D represent light bulbs.

Which of the following is true about these two circuits? Assume voltage sources have the same value and all the light bulbs are all identical.

Bulbs A and B have different brightnesses.

Bulbs A and B will be brighter than bulbs C and D.

Bulbs C and D have different brightnesses.

All bulbs will have the same brightness.

Bulb A will be as bright as bulb C, but bulbs B and D will have a different brightness.

Bulbs A and B will be brighter than bulbs C and D.

Explanation:

Since bulbs A and B are in parallel, they will have the same voltage, and since the bulbs are identical in resistance, they will have the same current running through them and will be just as bright.

Let's say the voltage source as a value of  and each bulb has a resistance of .

The current going through bulbs A and B is .

However, the current going through bulbs C and D is .

The current going through bulbs C and D is half as much as the other two, so their brightness will be less.

So, bulbs A and B will be brigher than bulbs C and D.

### Example Question #1 : Circuit Power

If the circuit above is connected to a  battery, what is the total power dissipated by the circuit?

Explanation:

The equation for power dissipated in a circuit is

The three resistors are in parallel with each other, so the total resistance is

Use Ohm's law to find current.

Finally, solve for power.

### Example Question #1 : Circuit Power

In the circuit above, find the power being dissipaited by .

None of these

Explanation:

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.

Because it is not in parallel, the total current in the circuit is equal to the current in .

The equation for power is as follows:

### Example Question #1 : Circuit Power

In the circuit above, find the power being dissipated by .

None of these

Explanation:

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.

The equation for power is as follows:

### Example Question #1 : Circuit Power

In the circuit above, find the power being dissipated by .

None of these

Explanation:

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.

The equation for power is as follows:

### Example Question #1 : Circuit Power

What can be said about the power being dissipated by  and ?

None of these

will dissipate more power than

will dissipate more power than

It is impossible to tell

Their values will be equal

Their values will be equal

Explanation:

and are in series with each other, therefore, they will have the same current values. They also have the same resistance values. Thus, they will have the same power dissipated, as .

### Example Question #10 : Circuit Power

Calculate the power being dissipated by

None of these

Explanation:

The first step is to find the total resistance of the circuit.

In order to find the total resistance of the circuit, it is required to combine all of the parallel resistors first, then add them together as resistors in series.

Combine  with with with .

Then, combining  with  and :

Ohms is used law to determine the total current of the circuit

Combing all voltage sources for the total voltage.

Plugging in given values,

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

Using ohms law:

It is also true that:

Using Subsitution:

Solving for :

Plugging in values:

Using the definition of electric power, where is current and is the resistance of the component in question.