Electrical Engineering: Basic Laws (15 of 31) Conductance in a Parallel Circuit

Summary

The video explains how to calculate current in parallel circuits using conductance, which is the inverse of resistance. Two resistors (12 ohms and 4 ohms) are analyzed, and their conductances are calculated. The key advantage of using conductance is that it simplifies current calculations, as current in each branch equals the conductance multiplied by the voltage. This approach is contrasted with the traditional method using resistance, showing how both yield the same total current. The video demonstrates that using conductance can make solving parallel circuits faster and easier.

Takeaways

• ⚡ Conductance is the inverse of resistance, and it is easier to use in certain circuit calculations.
• 🔌 In a parallel circuit, the voltage across each branch is always the same.
• 🧮 The conductance in each branch (G) is calculated as 1 over the resistance (R).
• 📐 Using Ohm's Law, current (I) is equal to conductance (G) multiplied by voltage (V).
• 🔄 For branch 1, G1 = 1 / 12 ohms, and for branch 2, G2 = 1 / 4 ohms.
• 💡 The current in the first branch is G1 times the voltage (20V), resulting in approximately 1.67 amps.
• ⚙️ The current in the second branch is G2 times the voltage (20V), giving 5 amps.
• 🔗 The total resistance in the parallel circuit is found using the product-over-sum formula: R_total = (R1 * R2) / (R1 + R2).
• 📊 The total resistance of the circuit is 3 ohms, and the total current is 6.67 amps.
• ✅ Using conductance simplifies finding the current in each branch compared to traditional resistance methods.

Q & A

What is conductance in relation to resistance?

Conductance is the inverse of resistance. It is a measure of how easily electricity flows through a component, and its unit is Siemens (S).

How is the current in a parallel circuit calculated using conductance?

The current in a parallel circuit is calculated by multiplying the conductance of each branch by the voltage across the branch. This is a simplified version of Ohm's law when using conductance.

What is the voltage across each branch in a parallel circuit?

In a parallel circuit, the voltage across each branch is the same. In this example, it is 20 volts across both branches.

How do you calculate the conductance of a resistor?

The conductance (G) of a resistor is calculated as the inverse of its resistance (R). For example, G1 = 1/R1.

What are the conductances of the two resistors in the example?

For the first resistor, G1 = 1/12 Siemens, and for the second resistor, G2 = 1/4 Siemens.

How do you calculate the current in each branch using conductance?

To calculate the current, multiply the conductance by the voltage. For the first branch, I1 = G1 * V, and for the second branch, I2 = G2 * V.

What is the total resistance in the parallel circuit example?

The total resistance is calculated using the product-over-sum formula: R_total = (R1 * R2) / (R1 + R2), which in this case equals 3 ohms.

How is the total current in the circuit determined using resistance?

The total current is found using Ohm's law, I = V / R. With a total voltage of 20 volts and a total resistance of 3 ohms, the current is 6.67 amps.

Does the sum of the branch currents match the total current of the circuit?

Yes, the sum of the branch currents (1.67 amps and 5 amps) equals the total current of 6.67 amps, confirming the calculations are correct.

Why is using conductance easier in parallel circuits compared to using resistance?

Using conductance simplifies the calculation of current in each branch because you only need to multiply the conductance by the voltage, avoiding more complex equations required with resistance.

Outlines

00:00

🔌 Understanding Conductance in Parallel Circuits

The script introduces the concept of conductance, which is the inverse of resistance. It explains how to calculate conductance (G) for two resistors in parallel, R1 and R2, with values of 12 ohms and 4 ohms respectively. The formula for conductance is G = 1/R, leading to G1 = 1/12 ohms and G2 = 1/4 ohms. The script then demonstrates how to calculate the current in each branch of a parallel circuit using the formula I = G * V, where V is the voltage across each branch. It uses Ohm's law in the form I = V/R and its inverse to find the current in each branch, showing that the current in the first branch (I1) is approximately 1.67 amps and in the second branch (I2) is 5 amps. The script also shows how to calculate the total resistance of the parallel circuit using the formula R_total = (R1 * R2) / (R1 + R2), resulting in 3 ohms. Finally, it verifies the current calculations by summing the individual branch currents and comparing it to the total current calculated using the total resistance.

Keywords

💡Conductance

Conductance is the measure of how easily electric current flows through a component. It is the inverse of resistance, meaning that a higher conductance corresponds to a lower resistance. In the video, conductance is used to simplify the calculation of current in parallel circuits. Instead of using resistance, the video explains how multiplying conductance by voltage directly gives the current in each branch.

💡Resistance

Resistance is a measure of how much a component opposes the flow of electric current. It is commonly used in circuit analysis. In the video, two resistors, R1 (12 ohms) and R2 (4 ohms), are in parallel, and their combined resistance is calculated to find the total current in the circuit. The video contrasts the use of resistance with conductance, showing that conductance simplifies current calculations in parallel circuits.

💡Parallel Circuit

A parallel circuit is a type of electrical circuit where components are connected across common points, sharing the same voltage. In the video, the two resistors (R1 and R2) are arranged in parallel, meaning they both experience the same voltage (20 volts). This setup allows for easier calculation of the current using conductance, as the voltage is constant across both branches.

💡Ohm's Law

Ohm's Law states that the current through a conductor between two points is directly proportional to the voltage across the two points and inversely proportional to the resistance. In the video, the formula is mentioned in its traditional form (I = V/R) and a modified form using conductance (I = G × V). The video applies Ohm’s Law to calculate currents and resistances in the parallel circuit.

💡Voltage

Voltage, also called electric potential difference, is the force that drives electric current through a circuit. In the video, the voltage across the entire circuit and across each branch of the parallel circuit is 20 volts. Since the voltage remains the same in a parallel circuit, it simplifies the calculation of current using conductance.

💡Current

Current is the flow of electric charge through a conductor, measured in amperes (amps). In the video, the current in each branch of the parallel circuit is calculated using both conductance and resistance. For example, the current in one branch is 1.667 amps, and in the other, it is 5 amps. The total current in the circuit is shown to be the sum of the two branch currents.

💡Siemens

Siemens (S) is the unit of measurement for conductance. It is the reciprocal of the ohm, which is the unit for resistance. In the video, the conductance of each branch is calculated in Siemens. For example, G1 (the conductance of the first branch) is 1/12 Siemens, and G2 (the conductance of the second branch) is 1/4 Siemens.

💡Total Resistance

Total resistance refers to the equivalent resistance of all components in a circuit. In the case of parallel circuits, the total resistance is calculated using the formula: product of the resistances divided by their sum. In the video, the total resistance of the two parallel resistors is calculated to be 3 ohms. This value is then used to determine the total current in the circuit.

💡Equivalent Circuit

An equivalent circuit is a simplified version of a complex circuit that has the same electrical characteristics. In the video, the two resistors in parallel are combined into an equivalent circuit with a total resistance of 3 ohms. This equivalent circuit is then used to calculate the total current flowing through the system using Ohm’s Law.

💡Branch

A branch in a circuit is a part where current divides and flows through different paths. In the video, there are two branches, each containing one resistor. The current in each branch is calculated separately, and then the two currents are added together to find the total current in the circuit. The concept of branches is crucial for understanding how parallel circuits function.

Highlights

Introduction to the concept of conductance and its inverse relationship with resistance.

Explanation of conductance in terms of Ohm's law with the formula I = G * V.

Description of a parallel circuit with two resistors, R1 and R2, each with different resistance values.

Calculation of conductance for each branch using the formula G = 1/R.

Explanation that voltage across each branch in a parallel circuit is equal.

Simplification of current calculation in parallel circuits using conductance.

Detailed calculation of current in the first branch (I1) using conductance G1 and voltage V.

Detailed calculation of current in the second branch (I2) using conductance G2 and voltage V.

Verification that the sum of individual branch currents equals the total circuit current.

Correction of a mistake in calculating total resistance using the formula for parallel resistors.

Calculation of the total resistance (R_total) of the parallel circuit.

Use of Ohm's law to find the total current (I) in the circuit using total resistance.

Confirmation that the sum of individual branch currents matches the total current calculated using resistance.

Advantage of using conductance over resistance for calculating current in parallel circuits.

Final summary of the method for finding current in each branch using conductance.

Emphasis on the ease and efficiency of using conductance in parallel circuit analysis.

Transcripts

welcome to electron line in this video

we're going to take a look at peril

circuits and conductance remember that

conductance was the inverse of

resistance so here we have two resistors

in parallel r1 equals 12 ohms R 2 equals

4 ohms G 1 which is a conducts

conductance in branch 1 is 1 over the

resistance and G 2 which is a

conductance since the second branch is

equal to 1 over the second resistor

remember that Ohm's law is equal to V

over R and since G is 1 over R we can

write I is equal to G times V so it's a

different form of Ohm's law if we now

want to calculate the current in each of

the two branches we can do it as follows

we realize that the voltage across each

branch is equal in a parallel branch and

in this case the 20 volts across the

source was also equal to 20 volts across

the first branch in the 20 volts across

the second branch normally when we use

resistors and current we have to come up

with a kind of complicated equation to

come up with the current but if we use

conductance instead it's actually really

easy to find the current in each branch

because it's simply the conductance

times the voltage you know the voltage

in the first branch is equal to 20 volts

the voltage in the second branch is

equal to 20 volts because the voltage

across any branch in the parallel

circuit is always equal to each other

and then calculating G 1 and G 2 G 1 is

equal to 1 over R 1 which is equal to 1

over 12

that would be Siemens because the unit

for conductors the Siemens and e 2 is

equal to 1 over R 2 and R 2 is 4 ohms at

1 over 4 Siemens so those are the due

conductances which means that the

current in the first branch is equal to

G 1 times V in this case G 1 is 1 over

12 Siemens times V which is 12 volts 12

divided by Sigma 12 divided by 20

divided by 12 22 5 by 12 is 1 points 6 7

1 points 6 6

I am salt two to three decimal places so

that's occurring the first branch and i2

is equal to e2 and zg2 is one over four

Siemens times twenty volts that's equal

to 20 divided by 4 which is 5.000 amps

there is the current and second branch

and that should add up to the current of

the circuit so if we try to find I using

the traditional method by using

resistances I'm going to find the total

resistance R oh yes I just saw that

thank you thank you for pointing it out

so this should be R 1 that R 2 and our

total is equal to the product over the

sum r1 times r2 divided by r1 plus r2

this is equal to 12 times 4 divided by

12 plus 4 which is equal to 48 divided

by 16 which is equal to 3 ohms so that's

the equivalent or total resistance in

the circuit now using Ohm's law I is

equal to V over R the total voltage 20

volts the total resistance 3 ohms which

is equal to 20 divided by 3 is six point

six six seven amps and that should be

the same as the sum of these two and a

quick inspection shows that five plus

one point six six seven is indeed six

point six seven so we know that these

are correct and it adds up to the total

current again you can see that if we use

conductance instead of resistance in

parallel circuits it actually makes it

easier to find the current in each of

the branches we simply multiply the

voltage of each branch which is equal to

the voltage across the branch times the

conductance in each branch that gives

you the current so it's a quick way to

find the current in a different method

that's how it's done