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Transcript
Series and
Parallel Circuits
Khemraj Nandanwar
T.G.T.(Work Experience)
Kendriya Vidyalaya,Golaghat
Circuits can either be
series or parallel.
Series Circuits:In Series circuit a number
of resistors are connected
end to end in such a way
that the same current flows
through each resistor.
Lights in a Series:-
By adding resistor in a
series circuit (Like the
another light):Total resistance goes UP since all the
current has must go through each resistor.
If you remove a light bulb or one burns
out—all go out!
Derivation for calulating Total resistance ,
Total Voltage, Individual voltages, Total
current (SERIES):The circuit in Figure shows three resistors
connected in series, and the direction of current
is indicated by the arrow.
 Note that since there is only one path for the current to
travel, the current through each of the resistors is the
same.

(Equation-1)
 Also, the voltage drops across the resistors must add
up to the total voltage supplied by the battery.


(Equation-2)
 Since V = I R, then

(Equation-3)
But Ohm's Law must also be satisfied for the
complete circuit

(Equation-4)
Setting equations [3] and [4] equal, we get-
We know what the current through each resistor
(from equation [1] is just I.
So the currents cancel on both sides, and we
arrive at an expression for equivalent resistance
for resistors connected in series.
In general, the equivalent resistance of resistors
connected in series is the sum of their
resistances. That is,
Resistance in SERIES circuits :The total or equivalent resistance (RT or Req)
for this combination is equal to the sum of the
individual resistors, i.e.,
 R T = R1+ R 2+ R 3
Add up all resistors to get Total Resistance.
Total resistance will go up because all of the
current must go through each resistor.
Example-1:- Find the total
resistance of a series circuit in which 6
ohms,5ohms and 4 ohms resistances are
connected.
Answer:Given data :R1=6Ω,
R2=5Ω and
R3=4Ω
RT=?
Total Resistance =RT

=R1+R2+R3

= 6+5+4

= 15 Ω
Therefore,Total Resistance=RT

=15 Ω
Voltage in SERIES circuits:In series circuit, the voltage is divided at each
resistance according to their value.
V1 -Voltage of resistance R1.
V2 – Voltage of resistance R2.
V3 – Voltage of resistance R3.
Total Voltage = V =V1+ V2+ V3

Parallel Circuits:-
In Parallel circuit a number of
resistors are arranged in such a
way that one end of each
resistor is connected to the
same one point and the other
end of the each resistor is
connected to another common
point.
Lights in Parallel
By adding resistor in a
parallel circuit :Total resistance goes down.
If you remove a light bulb or one
burns out, the others stay on because
the circuit is still closed.
Derivation for calulating Total resistance ,
Total Voltage, Individual voltage, Total
current (PARALLEL):Each of the three resistors in Figure is another
path for current to travel between points A and
B.
Each of the three resistors in the parallel circuit
must have the same voltage.

(Equation-1)
Also, the current splits as it travels from A to B.
So, the sum of the currents through the three
branches is the same as the current at A and at
B.

(Equation-2)
By Ohm's Law, equation [2] is equivalent to:

 By equation [1], we see that all the voltages
are equal.
So the V's cancel out, and we are left with
This result can be generalized to any number of
resistors connected in parallel.
Resistance in PARALLEL circuits :The formula for the equivalent resistance is as
follows:
1/R = 1/R1 + 1/R2 + 1/R3
Example-4:- Find the total
resistance of a parallel circuit in which
10 ohms and 20 ohms resistances are
connected.
Answer:Given data :
R1 = 10Ω,
R2 = 20Ω and
RT = ?
Total Resistance =1/RT

=1/R1+1/R2

= (1/10)+(1/20)

1/RT= 3/20

RT= 20/3

RT=6.67 Ω
Therefore,Total Resistance=RT

=6.67 Ω
Example-5:- If the resistances of 6
ohms,3 ohms are connected in
parallel. Total voltage is 48V.
Calculate the total current and
current through each resistance.
Answer:Given data :R1= 6 Ω,
R2= 3 Ω,
VT= 48V,
IT=?,I1=? And I2=?
 Total Resistance = 1/RT=(1/R1)+(1/R2)

=(1/6)+(1/3)

1/RT = 1/2

RT = 2 Ω
 Total Current = IT = VT/RT = 48/2 = 24 Amp.
 In Parallel VT = VI = V2 = V3
 I1=VT/ R1 = 48/6 = 8 Amp.
 I2=VT/ R2 = 48/3 = 16 Amp.
 OR
 In parallel circuit,
 Total Current=IT= I1 + I2

= 8 + 16 = 24 Amp.
Voltage in Parallel circuits:In parallel circuit, the voltage across each
resistor is the same, i. e.
V1 -Voltage of resistance R1.
V2 – Voltage of resistance R2.
V3 – Voltage of resistance R3.
Total Voltage = VT = V = V1 = V2 = V3