Electrical Engineering: Basic Laws (15 of 31) Conductance in a Parallel Circuit
Summary
TLDRThe 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
🔌 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.
Mindmap
Keywords
💡Conductance
💡Resistance
💡Parallel Circuit
💡Ohm's Law
💡Voltage
💡Current
💡Siemens
💡Total Resistance
💡Equivalent Circuit
💡Branch
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
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