# AP Physics 1 : Equivalent Resistance

## Example Questions

### Example Question #1 : Equivalent Resistance

Consider the following circuit:

What is the total equivalent resistance of the circuit?

Explanation:

First we need to condense R3 and R4. They are in series, so we can simply add them to get:

Now we can condense R2 and R34. They are in parallel, so we will use the following equation:

Therefore:

The equivalent circuit now looks like:

Since everything is in series, we can simply add everything up:

### Example Question #2 : Equivalent Resistance

Consider the given circuit:

What is the current through the system if we attach a  resistor from point A to B?

Explanation:

The new circuit has two resistors in parallel: R2 and the new one attached. To find the equivalent resistance of these two branches, we use the following expression:

In this new equivalent circuit everything is in series, so we can simply add up the resistances:

Now we can use Ohm's law to calculate the total current through the circuit:

### Example Question #1 : Equivalent Resistance

Consider the given circuit:

How much resistance must be applied between points A and B for the circuit to have a total current of 3A?

Explanation:

We will be working backwards on this problem, using the current to find the resistance. We know the voltage and desired current, so we can calculate the total necessary resistance:

Then we can calculate the equivalent resistance of the two resistors that are in parallel (R2 and our unknown):

Now we can calculate what the resistance between point A and B:

Rearranging for the desired resistance:

### Example Question #1 : Equivalent Resistance

Consider the circuit:

If the equivalent resistance of the circuit is  and each resistor is the same, what is the value of each resistor?

None of these

Explanation:

We can use the equation for equivalent resistance of parallel resistors to solve this equation:

We know the equivalent resistance, and we know that the resistance of each of the four resistors is equal:

### Example Question #5 : Equivalent Resistance

Consider the circuit:

If the power dissipated throughout the entire circuit is , what is the value of ?

Explanation:

Since we know the power loss and voltage of the circuit, we can calculate the equivalent resistance of the circuit using the following equations:

Substituting Ohm's law into the equation for power, we get:

Rearranging for resistance, we get:

This is the equivalent resistance of the entire circuit. Now we can calculate R4 using the expression for resistors in parallel:

### Example Question #6 : Equivalent Resistance

Consider the circuit:

If the current flowing through the circuit is , what is the value of R1?

Explanation:

We can use Ohm's law to calculate the equivalent resistance of the circuit:

Now we can use the expression for combining parallel resistors to calculate R1:

### Example Question #7 : Equivalent Resistance

Consider the circuit:

If the equivalent resistance of the circuit is , which of the following configuration of resistance values is possible?

None of these

Explanation:

We will need to test the values of each answer to find the one that generates an equivalent resistance of .

We know that when condensing parallel resistors, the equivalent resistance will never be larger than the largest single resistance, and will always be smaller than the smallest resistance. Therefore, two of the answer options cen be eliminated immediately.

After we have narrowed our choices down to the other options answers, we just have to test them with the following formula:

We will test the incorrect answer first:

### Example Question #8 : Equivalent Resistance

What is the equivalent resistance from Point A to Point B?

Explanation:

Because this circuit is neither purely series or purely parallel, we must simplify it before we solve it. Replace the right branch, which is purely series, with its equivalent resistance:

Now we have a purely parallel circuit, each branch having a resistance of . Apply the parallel formula and solve:

### Example Question #1 : Equivalent Resistance

What is the equivalent resistance of the following resistors, all in series: ?

Explanation:

For resistors all in series, the equivalent resistance is equal to the sum of the resistances.

### Example Question #1 : Equivalent Resistance

What is the equivalent resistance of a circuit consisting of a group of resistors (all in parallel), with the following resistances: ?