Combination of Resistors:
As the current in a circuit depends on the resister of the circuit. So, in the electrical circuits of TV, radio, mobile, and other things, it is usually necessary to combine two or more resistors to get the required current."Resistance" may sound negative, but in electricity, it can be used beneficially.Examples: Current must struggle to flow through the small coils of a toaster, enough to generate heat that browns bread. Old-style incandescent light bulbs force current to flow through filaments so thin that light is generated.
The resistance can be combined in two ways:
(I) In series
(ii) In parallel
1.Series combination:
In series equivalent resistance equals to total resistance connected in series. Req=R1+R2+R3...............etc. Example-Suppose this circuit in series have R1=100ohm, R2=300 ohm, R3=50 ohm then equivalent resistance of this series circuit is Req=R1+R2+R3=100+300+50=450ohm
Current in a series circuit is the same, only voltage is not, the voltage is additive to all circuit. In this circuit, you can see that current (I ) is the same everywhere but voltage (Veq=V1+V2+V3) is additive.
Resultant resistance of three resistors connected in series:
In this figure, three resistance R1, R2, R3 are connected in series. A battery of V volt has been applied to the ends of this series combination of resistances, the potential difference across the R1 is V1 and R2 is V2 and R3 is V3.
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| Series combination |
so Veq=V1+V2+V3 -------------(1)
By Ohm's law V=I x R
IReq=IR1+IR2+IR3-----------(2)
IReq=I(R1+R2+R3)-----------(3)
current is the same everywhere in the circuit, so canceling current both side
so we got Req=R1+R2+R3
Note-Thus, if three resistance R1, R2, R3 are connected in series then their total resistance Req is given by the formula. Req=R1+R2+R3
2.Parallel combination:
The combined resistance of a number of resistors connected in parallel can be calculated by using the law of combination of resistance in parallel. According to the law of combination of resistance connected in parallel is equal to the sum of the reciprocal of all the individual resistances. If a number of resistors R1, R2, R3.......etc. are connected in parallel, then the combined resistance Req is given by the formula.The total resistance of this circuit is
After cross multiplication
Req=3 ohm
"In the parallel circuit, voltage is the same(in terms of potential difference in the battery side) but the current(not the same) is divided according to the resistor connected in a parallel circuit."
Resultant resistance of three resistors connected in parallel
In the figure, three resistance R1, R2, R3 are connected parallel to one another between the same two points. A battery of V volts has been applied across the ends of this combination. In this case, the potential difference across the ends of the three resisters will be the same, the only current is the difference.
as we know the current is different
then Ieq=I1+I2+I3----------(1)
By ohm's law V=IR
so I=V/R put this value in eq (1)
(V is the same for all parallel-connected component)After canceling V from both sides
Note-Thus, if three resistance R1, R2, R3 are connected in parallel then their total resistance Req is given by the formula.