Greetings and welcome to practical ninjas.
In this video, we will be learning about resistors. Resistors are passive components that are
widely used in electrical and electronic circuits. But what is exactly a resistor or resistance?
Resistance as the name suggests is something that opposes flow of current. Resistance of
a conductor can be calculated if the length of the conductor, its area of cross-section
and the resistivity of the conductor material is known. Suppose the length is l, cross sectional
area is A and resistivity is rho, then the resistance of the conductor is given as R
=rho*l/A. From the formula we can infer that the resistance is directly proportional to
the length and inversely proportional to the cross-section area. Increasing the length
increases the resistance. The unit of resistance is ohms. This brings us to ohm’s law. Ohm’s
law states that the current flowing through a conductor is directly proportional to the
voltage applied across the conductor and inversely proportional to the resistance of the conductor.
Mathematically, it is written as V=I*R where V is the voltage and I is the current. To
understand voltage and current clearly check the video link for the same in the description. Using ohm’s law we can find out equivalent resistances across two terminals. Let us try
to find out equivalent resistance when resistors are connected as seen here. This kind of connection
is called as a series connection. As seen here, second resistor is connected to first
resistor at its end terminal. In series connection current flowing through the first resistance
passes through second resistance as there is no other path. If resistance values are
R1 and R2, then by ohm’s law voltage across R1 and R2 will be V1=IR1 and V2=IR2. Total
voltage applied will be V=V1+V2. V can be equated to IReq, where I is the total current
and Req is the equivalent resistance of the circuit. This V can also be equated to IR1+IR2.
Comparing both the equations we get Req=R1+R2. Same formula can be extended to n resistances
in series and it’s equivalent resistance can be calculated as Req=R1 + R2 + till
+Rn. This is called series equivalent resistance. Now consider the circuit shown in the figure.
Here, the resistances are connected on both the ends. This type of connection is called
as parallel combination. In the parallel combination, voltage applied across the terminals of resistors
remain same, however current through the resistors change. Let the total current be I and I1,
I2 be the currents through R1 and R2 respectively. Voltage across the resistors is V, then I1
=V/R1 and I2=V/R2. Suppose Req is the parallel equivalent, then I=V/Req. We know that I
=I1 + I2. This gives us 1/Req=1/R1 + 1/R2. This is the parallel equivalent resistance.
The same formula can be extended to n resistances in parallel. 1/Req=1/R1+1/R2+till 1/Rn.