Electrical Engineering: Basic Laws (13 of 31) Series Resistors and Voltage Division

Summary

The video explains the concept of a voltage divider in a series circuit. Using a 20-volt source and two resistors (4 ohms and 6 ohms), it demonstrates how to split the voltage into 8 volts and 12 volts across each resistor. The process involves calculating total resistance, current, and voltage drops using Ohm's law. The voltage divider can be used to reduce a voltage source for specific needs, such as powering a load resistor with the appropriate voltage. An alternative formula for voltage dividers is also introduced for more flexibility in designing circuits.

Takeaways

• 🔋 The circuit being discussed is a series circuit and a voltage divider using a 20-volt source.
• 🔧 The negative end of the voltage source is connected to ground, setting the voltage to 0V at that point.
• 🧮 The goal is to find the voltage drops across two resistors, labeled as V1 (across R1) and V2 (across R2).
• 🔌 A voltage divider allows the reduction of the overall voltage into smaller portions, suitable for other loads in a circuit.
• 📏 The total resistance in the circuit is the sum of the resistors R1 and R2, giving a total resistance of 10 ohms.
• ⚡ Using Ohm's Law, the current in the circuit is calculated as 2 amps, determined by dividing the voltage by the total resistance.
• 📐 The voltage drop across R1 (V1) is calculated as 8 volts, and the drop across R2 (V2) is 12 volts.
• 🔄 The circuit divides the 20V source into 8V and 12V across the resistors, matching the expected total voltage drop.
• 📉 Voltage dividers can be used to provide the correct lower voltage for different components or loads in a circuit.
• 📝 Another way to calculate the voltage across a resistor in a voltage divider is by using the ratio of the resistances, as shown in the final example using V2 = 20V * (6/10).

Q & A

What is a voltage divider?

A voltage divider is a circuit configuration that divides the input voltage into smaller output voltages using a series of resistors.

How is the total resistance in a series circuit calculated?

In a series circuit, the total resistance is the sum of the individual resistances. For this circuit, the total resistance is R1 + R2, which equals 4 ohms + 6 ohms = 10 ohms.

How do you calculate the current in a series circuit?

The current is calculated using Ohm's law: I = V / R, where V is the total voltage and R is the total resistance. In this case, I = 20V / 10 ohms = 2 amps.

How can you find the voltage drop across each resistor in the series circuit?

The voltage drop across each resistor is calculated using the formula V = I * R. For R1, the voltage drop is V1 = 2 amps * 4 ohms = 8 volts. For R2, the voltage drop is V2 = 2 amps * 6 ohms = 12 volts.

Why is this circuit called a voltage divider?

This circuit is called a voltage divider because it takes an input voltage (20V in this case) and divides it across two resistors, resulting in smaller voltages (8V and 12V).

What is the purpose of using a voltage divider in a circuit?

The purpose of a voltage divider is to reduce a higher input voltage to a lower output voltage, which can then be used to drive a load or another part of a circuit that requires a lower voltage.

What happens to the remaining 8 volts in the circuit after the voltage divider reduces the voltage to 12 volts?

The remaining 8 volts is not used in this particular case because the objective was to reduce the 20 volts down to 12 volts. The extra voltage does not need to be connected to anything.

How can you determine the voltage across a specific resistor using the ratio of resistances?

You can determine the voltage across a resistor in a voltage divider by using the formula V2 = V * (R2 / (R1 + R2)). In this case, V2 = 20V * (6 ohms / (4 ohms + 6 ohms)) = 12 volts.

What role does grounding play in this circuit?

Grounding ensures that the negative end of the voltage source is set to 0 volts, providing a reference point for the circuit and ensuring that the voltage drops can be calculated accurately.

Why is Ohm's law important in analyzing this circuit?

Ohm's law is important because it allows you to calculate both the current through the circuit and the voltage drops across the resistors, which are key to understanding how the voltage divider works.

Outlines

00:00

🔌 Introduction to Series Circuit and Voltage Divider

The video begins with an introduction to a series circuit and the concept of a voltage divider. A 20-volt source is connected to a circuit consisting of two resistors. The negative end of the voltage source is connected to the ground, setting the reference point to 0 volts. The goal is to find the voltage drop across resistors R1 and R2, which are labeled as V1 and V2, respectively. The voltage divider helps reduce the 20-volt source to a lower voltage, which can be used to power other components.

📐 Total Resistance and Current Calculation Using Ohm’s Law

The circuit consists of two resistors: R1 (4 ohms) and R2 (6 ohms). Since this is a series circuit, the total resistance (R_total) is the sum of R1 and R2, which equals 10 ohms. Using Ohm's Law (V = IR), the total current (I) in the circuit is calculated by dividing the supplied voltage (20 volts) by the total resistance (10 ohms), resulting in a current of 2 amps flowing through the circuit.

🔋 Voltage Calculation Across R1 and R2

With the current determined, the video explains how to calculate the voltage drops across each resistor using Ohm's Law (V = IR). The voltage drop across R1 (V1) is calculated as 2 amps multiplied by 4 ohms, resulting in 8 volts. Similarly, the voltage drop across R2 (V2) is 2 amps multiplied by 6 ohms, giving 12 volts. The total voltage drop across both resistors sums to the 20 volts provided by the source.

📉 Voltage Divider and Its Function

The concept of the voltage divider is further explained. The 20-volt source is divided into an 8-volt drop across R1 and a 12-volt drop across R2. The video highlights how the voltage divider can be used to lower the voltage for specific components, such as a load resistor that requires less than 20 volts. By selecting the appropriate resistor values, the desired voltage for the load resistor can be achieved.

🔧 Alternative Voltage Divider Equation

An alternative method to calculate the output voltage across a resistor in a voltage divider is introduced. The output voltage (V2) can be found using the formula V2 = V_total * (R2 / (R1 + R2)), where V_total is the input voltage. In this case, V2 is calculated as 20 volts multiplied by the ratio of R2 (6 ohms) to the total resistance (10 ohms), which results in 12 volts. This provides another way to quickly determine the voltage output of a voltage divider circuit.

Keywords

💡Series Circuit

A series circuit is an electrical circuit where the components are connected end-to-end, so that the same current flows through each component. In the video, the speaker explains how the resistors are connected in series, meaning the current flows through both resistors one after the other. This setup is essential for creating a voltage divider.

💡Voltage Divider

A voltage divider is a circuit that divides the input voltage into smaller output voltages. It uses a combination of resistors to proportionally reduce voltage. The video describes how a 20-volt source is divided into 8 volts across one resistor and 12 volts across another resistor, which is a practical use of the voltage divider in circuits.

💡Voltage Drop

Voltage drop refers to the reduction in voltage across a component in a circuit. In the video, the speaker calculates the voltage drops across two resistors, R1 and R2, showing that the 20-volt total is divided into 8 volts and 12 volts across the resistors, respectively.

💡Resistor

A resistor is a passive electrical component that limits the flow of current in a circuit. In the video, two resistors are used in series to create the voltage divider, with their individual resistances determining how the 20 volts are divided across them. R1 has 4 ohms, and R2 has 6 ohms of resistance.

💡Ohm's Law

Ohm's Law states that the current (I) in a circuit is equal to the voltage (V) divided by the resistance (R). The speaker uses Ohm's Law to calculate the current in the circuit and the voltage drops across the resistors, highlighting how the law governs the relationships between voltage, current, and resistance.

💡Current

Current is the flow of electric charge in a circuit, measured in amperes (amps). In the video, the current is calculated to be 2 amps using Ohm’s Law, based on a 20-volt source and a total resistance of 10 ohms in the series circuit. The current remains constant throughout the circuit in a series configuration.

💡Total Resistance

Total resistance in a series circuit is the sum of the individual resistances. In the video, the speaker calculates the total resistance by adding R1 (4 ohms) and R2 (6 ohms), resulting in 10 ohms. This total resistance is then used to find the current in the circuit using Ohm’s Law.

💡Load Resistor

A load resistor is a resistor connected to the output of a circuit to draw power or perform work. In the video, a load resistor is mentioned as being placed across the voltage divider to operate at a lower voltage, such as 12 volts, which is made possible by the voltage divider configuration.

💡Node

A node is a point in a circuit where two or more components are connected. In the video, the speaker refers to a node at the connection point between R1 and R2, which helps determine the voltage levels at different parts of the circuit. This node is crucial for understanding the division of voltage.

💡Ground

Ground refers to a reference point in an electrical circuit from which voltages are measured, typically considered to be at zero volts. In the video, the negative terminal of the voltage source is connected to ground, ensuring that the circuit has a defined voltage reference for calculating voltage drops across the resistors.

Highlights

Introduction to a series circuit and voltage divider concept.

20-volt source connected with negative end to ground.

Objective to determine voltage drop across V1 and V2.

V1 and V2 represent voltage drops across R1 and R2 respectively.

Explanation of voltage divider's ability to create lower voltages.

Potential to add a load resistor to V2 for lower voltage requirements.

Calculation of total resistance in a series circuit.

Use of Ohm's law to find the current in the circuit.

Determination of current as 2 amps in the circuit.

Calculation of voltage across R1 using Ohm's law.

Calculation of voltage across R2 using Ohm's law.

Verification of voltage drops summing up to the source voltage.

Explanation of how the voltage divider divides 20 volts into 8 and 12 volts.

Practical application of voltage dividers in circuit boards.

Discussion on utilizing the lower 8 volts if needed.

Alternative method for calculating voltage across R2 using resistor ratios.

Formula for determining the correct resistor combination for a desired voltage.

Conclusion on how voltage dividers are used to adjust voltage for specific applications.

Transcripts

welcome to electron line now we're going

to take a look at a series circuit and

what we also call a voltage divider here

we have a 20 volt source here are the

output terminals of the of the source

also notice that we've connected the

negative end of the voltage source to

grant which means we force out to be

zero volts and now what we're trying to

determine is what is the voltage drop

across v1 and what is the voltage drop

across v2 v1 is the voltage drop across

R 1 and v2 is the voltage drop across R

2 the reason why we call this a voltage

dividers because we can take a 20 volt

source and with a combination of two

resistors like this determine or turn

this into a lower voltage onto which we

can we can actually put a other load for

example we could put a low resistor and

drive it better here there we go here's

my load resistor we could put a low

resistor on v2 if the load resistor

requires a voltage less than the 20

volts and by picking the right

combination of r1 and r2 we can that we

can then make this to be the correct

voltage for the particular reason that

we want it for the way we do that is we

first find the total resistance in the

circuit our total and make in this case

instance a series circuit is simply the

sum of the two resistors r1 plus r2

which is equal to 4 ohms plus 6 ohms

which is equal to 10 ohms from that

using Ohm's law we can find the current

in the circuit so the current I can be

determined using Ohm's law to be the

voltage supplied divided by the total

resistance in this case that's 20 volts

divided by 10 ohms which is equal to 2

amps so the current here is equal to 2

amps now we can find the voltage across

r1 in the voltage across r2 again using

Ohm's law we can then take this equation

we can take I equals V over R and write

it as V equals I times R so the voltage

across any resistor simply the current

through the resistor times the

resistance

v1 is equal to r1 or I won so I times R

1 which is 2 amps times 4 ohms which is

8 volts and v2 is equal to I times R 2

which is equal to 2 amps times 6 ohms

which is equal to 12 volts which means

since a must be a 20 volt because this

end of the voltage source is 20 volts

higher than this end which is a zero

volt that may exist at 20 volts then we

have V 1 and 8 volt drop 20 volts minus

8 puts this at 12 volts so this is at 20

volts this is at 12 volts and then we

have a 12 volt drop across r2 from 12

down to 0 volts this of course should be

the same as the voltage over here

because this is a single node right here

which is attached to ground what that

means now is that we've we have a

voltage divider where we took 20 volts

and divided into 8 volts and 12 volts

and if you want the low resistance be

connected to 12 volts we have the right

voltage divider and this then provides a

12 volts for the resistor this is if

this is the technique that is often used

in circuitry on circuit boards what do

we do with the other 8 volts well we can

utilize the 8 volts or gas in Class A we

don't need it we don't need to attach an

into it we were just interested in

taking a 20 volt source and bring it

down to 12 volt that we can apply to a

low resistor and that's what we're after

one more quick note on this another way

of dealing with voltage dividers if for

example we want a specific voltage right

here volt 2 volt ooh that can be written

as the voltage applied by the voltage

source times the ratio of R to the

resistance across this particular

connection divided by the sum of the two

resistors this case v2 is equal to the

20 volts times the ratio of 6 ohms

divided by 4 plus 6 ohms 4 ohms plus 6

ohms

6/4 4 + 6.6 divided by 10 or 20 volts

times 6 over 10 which is equal to 12

volts so it's another way in which you

could look at a voltage divider simply

by using this equation right here we can

determine what combination resistors we

need pick them up with the correct

voltage on our voltage divider how it's

done