# AP Physics 1 : Equivalent Resistance

## Example Questions

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### Example Question #45 : Circuits

Consider the given circuit diagram. If each resistor has a resistance of  and the voltage source is , what is the current flowing through resistor B?

Explanation:

In this question, we're presented with a circuit diagram. We're told the values of the voltage source as well as each of the three resistors. We're asked to find the current that is flowing through resistor B.

To begin this problem, we'll need to figure out how much current is flowing through the entire circuit. But before we can do this, we'll need to figure out what the equivalent resistance of the circuit is. To do this, we'll need to look at how the circuit is configured so that we can see which resistors are in series, and which are in parallel.

We can see that resistors A and B are in parallel with each other. Furthermore, both A and B are in series with resistor C. So to begin, we'll need to find the equivalent resistance for resistors A and B. Using the equation for parallel resistors, we can calculate the equivalent resistance for resistors A and B.

Now that we've found the equivalent resistance for A and B, we can use this value in combination with resistor C, which is connected in series.

Because we've considered all the resistors in the circuit, this value is the total resistance of the circuit. Now, we can use Ohm's law in order to find the current running through the circuit.

Now that we have the total amount of current flowing through the circuit, we can look at each individual resistor in order to determine the amount of current flowing through that resistor. We can see that after traveling past the voltage source, there is a node that branches off, leading to resistor A and B. Because each of these resistors has the same resistance, the current through each must also be the same. Therefore, the current will split in half at the node, causing half the current to go to resistor A, and the other half to go to resistor B. Thus, the current flowing through resistor B is .

### Example Question #46 : Circuits

Consider the circuit diagram shown below.

If each resistor has a resistance of , then what is the equivalent resistance for the entire circuit?

Explanation:

In this question, we're presented with a circuit that has a number of resistors connected in series and in parallel, and we're asked to find the total resistance of the circuit.

In looking at this diagram, the first thing that we need to do is find the equivalent resistance for each group of resistors that are connected in series, which is the top two rows. And remember, resistors add directly when arranged in series.

Then, we can do the same thing for the middle row.

Now that we have a value of resistance for each row, we can now consider all three rows together as being connected in parallel. Remember, resistors arranged in parallel will add inversely.

### Example Question #47 : Circuits

You are given the following circuit:

The resistor values are as follows:

Find the equivalent resistance.

Explanation:

In order to find the equivalent resistance, you must take small steps and slowly work towards finding the total equivalent resistance.You can combine resistors if they are in parallel. The expression to find parallel equivalent resistance is:

You can also combine resistors in series, or one after the other. The expression to find resistors in series is:

To start off, you can combine R2 and R3, since they are both in parallel:

Next, you can combine some of the series resistors together.

After this, you can combine the following resistors in parallel:

Then, combine  and  in series:

Now get rid of the last parallel by combining  and  in parallel:

Now finally, add the remaining resistors in series to find the equivalent resistance:

### Example Question #21 : Equivalent Resistance

A circuit contains three resistors. Two of the resistors are in parallel with each other, and the third is connected in series with the parallel connection. If all the resistors' resistances must add to , what resistance should the resistor in series have to minimize the equivalent resistance?