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.