In this lecture, I am going to teach you all about resistance in power circuits, how to determine
the total resistance in power circuit, to calculate the equivalent resistance of a power circuit.
First, to know that the total current is the sum of the current is through the branches.
So the total current is shown in this circuit is the current of the battery IBI and this total current
will be divided into three tranches because we have three branches here.
So submission of this current is equal to the total current.
So I battery equal to i1 plus i three plus I.
For now we wanted to determine the total resistance.
We only know if the voltage in power circuit the voltage in each individual branch equal to the voltage
of the source.
The voltage in power circuit is identical.
Right is the thing.
So we will use ohm zero.
So current equal to voltage divided by resistance substitute in this equation to get the resistance
value.
So the total current is equal to a voltage of the source divided by the total resistance.
Right.
And the current I1 flow and resistor are one equal to the voltage of the source divided by in the resistor
are one and the current are three equal to the voltage of the source.
Divided by resistance are two and current I4 four equal to the voltage of the battery.
Divided by resistance are three.
Right.
We can divide both sides by the battery or we can write the equation like this.
The battery is equal to.
We can take the battery as a common.
From this side it is the same value.
So we battery multiplied by one divided by or one plus one divided by r two.
Plus one divided by or three.
And we have here we were three divided by our thought.
So we will divide this side by the battery.
And this site also will be divided by the battery.
So we battery divided by the battery equal to one and we battery in this side divided by the battery
equal to one.
So one divided by our total is equal to one divided by our one plus one divided by are two plus one
divided by are three.
Now we want you to get our total so we will take the reciprocal of both sides.
So the reciprocal of n is equal to one divided by n, so one divided by one divided by our total equal
to one divided by one over or one plus one over are two plus one.
Over are three in this side the.
Donator will become a nominator.
So one divided by one divided by our total is equal to our total divided by one.
So our total is equal to one over one divided by r one plus one divided by r two plus one divided by
r three.
And this is how to calculate the total resistance in per circuit.
So if we have four power resistors in a circuit, for example, how we get the total resistance, simply
we will add here one divided by or four if we have five branches.
So we will add here one divided by or five, so on.
Let's apply an example.
Find the equivalent resistance of the circuit shown here.
So our total equal to one divided by submission of the reciprocal of individual resistances here r one
is equal to one.
So substitute in zero one divided by one plus one divided by r two and r two is equal to two ohms,
so it is one half plus one divided by our 3r3 is equal to three ohms, so this part is one third.
So the total resistance here is equal to oh point 54 ohms.
You will notice from this example in a power circuit, the total circuit resistance is always less than
the smallest individual resistance.
The smallest individual resistance in this circuit is equal to one, and the total resistance of this
circuit is equal to 0.5.
So the total resistance here is less than or one.
If you made your calculation and, and the the total resistance in power circuit was greater than the
smallest individual resistance in the circuit.
So your calculation is wrong.
Check it again.
Another example we have here, a circuit and we have two identical resistors to resistor have the same
value.
When all resistors have the same resistance at the equivalent circuit, resistance is found by dividing
the resistance of one resistive element by the total number of resistors in parallel.
So the equivalent resistance in this example will equal to five ohms divided by two because we have
two branches.
So five divided by two is equal to 2.5 ohms.
As you learned in previous slides, our total is equal to one divided by one divided by R one plus one
divided by R two.
Here we will apply this formula in our example.
So one divided by one and r one is equal to five ohms plus.
R two is five ohms also.
So this equal to one divided by a we can take five as a common here in the denominator because it is
a submission.
So five divided by five is equal to one one because this is a submission.
So plus five divided by five is equal to one.
So this equal to one divided by two divided by five.
So there are five in the denominator here will become in the numerator.
So R to tell will equal to five divided by two.
If we have a circuit and this circuit has three resistors of five ohms, what is the total resistance
of this circuit?
So our total all equal to five divided by three ohms if we have four branches.
Each one five home.
So the total resistance will equal to five divided by four homes.