# Resistors in a Circuit

## Exercise One: Resistors in a Series Circuit

### Background Knowledge:

How to draw a Schematic

How to read and use a Multimeter

## What you'll need:

1 - 9 Volt Battery

1 - 9 Volt Battery Harness

1 - Breadboard

1 - 220-Ohm 1/4 Watt THR

1 - 470-Ohm 1/4 Watt THR

1 - 1 K-Ohm 1/4 Watt THR

1 - 10 K-Ohm 1/4 Watt THR

In this exercise you will learn how loads behave in a series circuit. A simple load in electronics is a resistor. The breadboard circuit you are going to build is a 9V Battery in series with four resistors. The resistor color bands in order are:

R1: Yellow- Purple- Brown- Gold

R2: Red- Red- Brown- Gold

R3: Brown- Black- Red- Gold

R4: Brown- Black- Orange- Gold

### Steps

Draw the schematic diagram and label the components.

When labeling your components in a circuit each resistor will be R#, so in this circuit R1, R2, R3, and R4. R1 will typically be the resistor closest to the positive node.

Your circuit should also have the nominal values of each component annotated on the schematic diagram. With Resistors, you can find this using the Resistor Color Codes.

Using what we know about current, you should also label the schematic with the anticipated current flow direction.

Find the measured values for each resistor.

Use your multimeter to check that each resistor is within its tolerance range set by its tolerance band. Set your multimeter to its ohm settings and make sure no power is applied to the circuit- on most multimeters you will break them if power is running through a circuit while measuring resistance. If you are using a multimeter that is not auto-ranging, set it to the closest resistance range that is not lower than your anticipated resistance load.

3. Add the total resistance of the series circuit.

The adding resistors in a series circuit formula is shown below. Remember, since there is only one path in this circuit, the formula is simply adding every resistor in its path.

4. Find Current.

Using Ohm's Law, you can calculate the current using the total voltage available divided by the total resistance to find total theoretical current.

Measure current in the circuit with your multimeter. To do this, you have to physically disrupt the circuit to insert your multimeter leads. If you are using a multimeter that is not auto-ranging, set it to the closest current range that is not lower than your anticipated current from your calculations.

5. Find Total Power.

You can use this information to find total power using the Power Formula, P=IV. The point of finding power is to make sure that power does not exceed the power rating on any individual component- For now, if the total power consumed in the circuit is less than a quarter watt, we can be 100% confident that it does not exceed the power rating of any individual component.

### Questions:

Are your percent errors within the ranges of the tolerance band on the resistors?

What is the total resistance of this circuit?

Is the measured resistance total close to the calculated resistance total using the nominal values?

How does current flow in a series circuit?

Why is calculating power before building any circuit important?

## Exercise Two: Measuring Voltage Drops in a Series Circuit

### Background Knowledge:

How to read and use a Multimeter

Current Flow and Voltage Drops in a Series Circuit

## What you'll need:

1 - 9 Volt Battery

1 - 9 Volt Battery Harness

1 - Breadboard

1 - 1N4007 Rectifier Diode

1 - 470-Ohm 1/4 Watt THR

1 - Red 5mm LED

Like a waterfall, electricity goes from the top to the bottom. The resistor and LED both use up part of the voltage- together, they use up all the voltage. The 470-ohm resistor uses up enough voltage so that the LED won't burn out but not too much so that the LED won't light up.

*A Safety Diode is not a consumer of voltage, so in theory, it should not make a voltage drop, but in real life, because the current is flowing through the material and most materials have some resistance, there is a small voltage drop- usually negligible.*

Let's look at how the Voltage is being used in the circuit.

### Steps

Draw the schematic diagram and label the components.

The first component in this circuit is a Safety Diode. This can be annotated as D#. D1 will typically be the diode closest to the positive node. In a circuit each resistor will be R#. R1 will typically be the resistor closest to the positive node. The last component in this circuit is an LED. This can be annotated as LED#. LED1 will typically be the LED closest to the positive node. In a circuit each resistor will be R#.

Your circuit should also have the nominal values of each component annotated on the schematic diagram. With Resistors, you can find this using the Resistor Color Codes.

Using what we know about current, you should also label the schematic with the anticipated current flow direction.

2. Find the measured values for the resistor.

Use your multimeter to check that the resistor is within its tolerance range set by its tolerance band. Set your multimeter to its ohm settings and make sure no power is applied to the circuit- on most multimeters you will break them if power is running through a circuit while measuring resistance. If you are using a multimeter that is not auto-ranging, set it to the closest resistance range that is not lower than your anticipated resistance load.

3. Record your power source voltage.

Measure it with the multimeter. Just because the battery is a 9V battery does not mean it is exactly 9-volts.

Set your multimeter to Direct Current Voltage (DCV). If you are using a Multimeter that is not auto-ranging, set it to the closest Voltage range the is not lower than your voltage source. In this case, we will be using a 9V battery, so most multimeters will have a 10 or 20 VDC range.

4. Measure the voltage drops over the following points:

To measure a voltage drop, place the red and black probes of the multimeter on either side of the required component. Polarity matters. The red (positive) probe should be in front of the component on the positive side, otherwise, your multimeter will read negative.

Across the safety diode.

Across the 470-ohm resistor.

Across the LED

5. Now add all of the voltages from step four.

Compare voltages added from step four to the recorded measured voltage from step three. When adding voltage drops in a series circuit, you can simply add each value together to get total voltage.

Calculate Percent Error of Voltage. Your percent error is your actual reading of the battery voltage compared to the sum of the voltage drops over the components. This difference is due to an efficiency loss of energy to heat and the current flowing through the wires and components.

6. Find Current.

Measure current in the circuit with your multimeter. To do this, you have to physically disrupt the circuit to insert your multimeter leads. If you are using a multimeter that is not auto-ranging, set it to the closest current range that is not lower than your anticipated current from your calculations.

7. Estimate resistance of the diodes.

Diodes have variable resistance determined by the amount of current flowing through them. Since we cannot measure their resistance while current is flowing because we will break most multimeters, the best we can do is calculate them using Voltage drops and Ohm's Law.

Now that we know the voltage drop over each component and the total current of the series circuit, use Ohm's law to estimate what the resistance of the safety diode and LED.

8. Find the power consumption of the circuit and all individual components.

This is to make sure the power consumption of a component does not exceed its safety rating. To find total power, you can use total current multiplied by total voltage.

In a series circuit, every component in the series circuit will have a different voltage drop and therefore consume a different amount of power. The new power formula for individual components becomes: Power equals the voltage drop of a component multiplied by the current through the component.

Calculate Percent Error of Power when you compare the total power consumption and the sum of the individual powers.

### Questions:

Why does each voltage drop of the components have to add up to total voltage? What if they aren't exact? Why would that happen?

How do voltage drops affect power over a component?

Would the four resistors in series from Exercise One have had a voltage drop over each of them?

Does any component in this circuit exceed its power safety rating? (Resistor's Power Rating: .25 Watt, LED's Power Rating: .2 Watt)

## Exercise Three: Resistors in a Parallel Circuit

### Background Knowledge:

How to read and use a Multimeter

## What you'll need:

1 - 9 Volt Battery

1 - 9 Volt Battery Harness

1 - Breadboard

1 - 1N4007 Rectifier Diode

1 - 1 K-Ohm 1/4 Watt THR

1 - 2.2 K-Ohm 1/4 Watt THR

1 - 10 K-Ohm 1/4 Watt THR

1 - 68 K-Ohm 1/4 Watt THR

In this exercise you will learn how loads behave in a parallel circuit. In a parallel circuit current flows differently than when it is in series since there is more than one path it can flow. Voltage also has some unique behavior and traits and Resistance is diminishing. The breadboard circuit you are going to build is a 9V Battery in parallel. The resistor color bands in order are:

R1: Brown- Black- Red- Gold

R2: Red- Red- Red - Gold

R3: Brown- Black- Orange- Gold

R4: Blue- Gray- Orange- Gold

Draw the schematic diagram and label the components.

When labeling your components in a circuit each resistor will be R#, so in this circuit R1, R2, R3, and R4. R1 will typically be the resistor closest to the positive node.

Your circuit should also have the nominal values of each component annotated on the schematic diagram. With Resistors, you can find this using the Resistor Color Codes.

Using what we know about current, you should also label the schematic with the anticipated current flow direction.

Find the measured values for each resistor.

Use your multimeter to check that each resistor is within its tolerance range set by its tolerance band. Set your multimeter to its ohm settings and make sure no power is applied to the circuit- on most multimeters you will break them if power is running through a circuit while measuring resistance. If you are using a multimeter that is not auto-ranging, set it to the closest resistance range that is not lower than your anticipated resistance load.

Note: Unlike the series circuit from above, you have to measure each resistor with the multimeter while not attached to the rest of the circuit unless you are measuring total resistance.

3. Add the total resistance of the parallel circuit.

The adding resistors in a parallel circuit formula is shown below. Remember, since there is more than one path in this circuit for current to flow, the formula for parallel resistance is diminishing.

4. Find Current.

Using Ohm's Law, you can calculate the current using the total voltage available divided by the resistance of each leg to find current through each branch. Remember, series circuits have the same voltage but unique currents down each branch.

Measure current in the circuit with your multimeter. To do this, you have to physically disrupt the circuit to insert your multimeter leads. If you are using a multimeter that is not auto-ranging, set it to the closest current range that is not lower than your anticipated current from your calculations. Since you have four branches, you will have to do this four times.

5. Find the total power consumption of the circuit and all individual components.

This is to make sure the power consumption of a component does not exceed its safety rating. To find total power, you can use total current multiplied by total voltage.

In a truly parallel circuit, every component in the parallel circuit will have a same voltage over each branch. Since this is a truly parallel circuit, we do not call this a "voltage drop." However, since each branch has its own unique current, each branch will consume a different amount of power. You will have to do this four times since there are four branches.

Add the four powers from the four branches to find total power of the circuit.

### Questions:

Why do you have to take the resistors out of the bread board to measure individual resistance in a truly parallel circuit?

Does total current of the circuit equal the sum of the added individual currents of each leg when using Ohm's Law for both?

Why does knowing the total power consumption still important even if it does not exceed the power rating of the circuit?

## Exercise Four: The Effects of Resistors in a Combination Circuit

### Background Knowledge:

How to read and use a Multimeter

Current Flow and Voltage Drops in a Series Circuit

## What you'll need:

1 - 9 Volt Battery

1 - 9 Volt Battery Harness

1 - Breadboard

1 - 1N4007 Rectifier Diode

1 - 220-Ohm 1/4 Watt THR

1 - 470-Ohm 1/4 Watt THR

1 - 2.2 K-Ohm 1/4 Watt THR

1 - 10 K-Ohm 1/4 Watt THR

1 - 47 K-Ohm 1/4 Watt THR

1 - 220 K-Ohm 1/4 Watt THR

6 - Red 5mm LED

Let's go back to the breadboard and see how different resistors affect a simple circuit. The resistor and LEDs are both loads. The resistor uses most of the voltage but usually leaves just enough for the LED to work. LEDs have variable resistance depending on the current running through them. Typically, this resistance causes them to use about 2 volts but can vary depending on the total current in a circuit. To see this, we can experiment with what would happen if you changed the resistors on the circuits?

You will measure the voltage used across the resistor and measure the voltage used across the LED. To measure a voltage drop, place the red and black probes of the multimeter on either side of the required component. Polarity matters. The red (positive) probe should be in front of the component, closest to the power source, otherwise, your multimeter will read negative. Using everything we know from the exercises above, you should be able to fill out this entire table through measuring with your multimeter or calculating using Ohm's Law and the Power Formulas.

Your setup should look like the breadboard to the left. Have your resistors arranged from lowest to highest value as represented in the table below.

Remember, for most multimeters, there is no power on the circuit when measuring resistance.

### Questions:

What is the relationship between resistance and voltage? Do you notice a trend forming?

Why does the LED get dimmer?

Does the amount of power consumed by the resistor and LED have any relationship to their resistances?

Using the relationship between voltage, current, and resistance could you find out the resistance of the LEDs? If so, what would be the resistance of the LED in series with the 470-Ohm Resistor?