# AP Physics 1 : Equivalent Resistance

## Example Questions

### Example Question #1291 : Ap Physics 1

Three identical resistors connected in parallel have an equivalent resistance equal to . What is the resistance of each of the individual resistors in this circuit?

Explanation:

In the question stem, we're told that a circuit containing three identical resistors connected in parallel has an equivalent resistance equal to . We are then asked to solve for the resistance of each individual resistor.

To start with, it's important to remember that resistors in parallel add inversely. Thus, the inverse of the equivalent resistance is equal to the sum of the inverse of each individual resistor. Put another way:

Since we know the three resistors we're dealing with are identical, we can assign each of them a value of .

And rearranging, we obtain:

### Example Question #71 : Electricity

Two resistors,  and , are connected in parallel.  What is the equivalent resistance of this setup?

Explanation:

The equivalent resistance of resistors connected in parallel is given by the following equation,

In our problem,

### Example Question #11 : Equivalent Resistance

Two resistors,  and , are connected in series.  What is the equivalent resistance of this setup?

Explanation:

The equivalent resistance of resistors connected in series is the sum of the resistance values of each resistor, or

In our problem,

### Example Question #1294 : Ap Physics 1

Three resistors, , and , are connected in series.  What is the equivalent resistance of this setup?

Explanation:

The equivalent resistance of resistors connected in series is the sum of the resistance values of each resistor, or

In our problem,

### Example Question #1295 : Ap Physics 1

Three resistors, , and , are connected in parallel.  What is the equivalent resistance of this setup?

Explanation:

The equivalent resistance of resistors connected in parallel is given by the following equation,

In our problem,

### Example Question #1296 : Ap Physics 1

Three resistors are connected to a battery. What is the equivalent resistance of the given circuit?

Explanation:

Remember the rules of adding resistors. For  resistors in series,

and for  resistors in parallel,

The idea is to start from the side furthest away from the battery and work back toward it. Notice that  and  are in parallel. We can add them in parallel so that they have an equivalent resistance ,

This can be calculated, but for 3 resistors we can leave it in equation form until the end. This looks like:

Notice that  is now in series with ,

### Example Question #41 : Circuits

A circuit has 10 identical resistors in parallel with a battery of , and a total resistance of . Determine the voltage drop across one resistor.

Explanation:

Since the resistors are in parallel to a  battery, the voltage drop across each resistor has to be equal to the voltage gain across the battery. Therefore, the voltage drop for any of the resistors will be .

### Example Question #42 : Circuits

Calculate the equivalent resistance, of four resistors in parallel, which values .

Explanation:

In order to find the equivalent resistance of resistors in parallel, we add the inverses of their values, as shown below

Finally

### Example Question #43 : Circuits

How does adding an additional resistor to a parallel circuit affect the equivalence resistance, or total resistance of the circuit?

Decreases the equivalent resistance

Has no effect on the equivalent resistance

Increases the equivalent resistance

Cannot be determined unless the resistance of the new resistor is known

Decreases the equivalent resistance

Explanation:

We can answer this by looking at how the equivalent resistance of a parallel circuit is calculated.

.

What we can see is that because the inverses are being added, any additional resistors will make contributions to the denominator of the fraction. Thus, lowering, or decreasing the equivalent resistance of the circuit.

### Example Question #44 : Circuits

Consider the following resistors in a circuit: . How should the resistors be connected in order to maximize the equivalent resistance of the circuit?

Parallel

Some combination of parallel and series

Series

Cannot be determined without knowing the voltage of the source