Electrical Engineering: Basic Laws (13 of 31) Series Resistors and Voltage Division
Summary
TLDRThe 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
🔌 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.
Mindmap
Keywords
💡Series Circuit
💡Voltage Divider
💡Voltage Drop
💡Resistor
💡Ohm's Law
💡Current
💡Total Resistance
💡Load Resistor
💡Node
💡Ground
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
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