Resistors are
connected in series when current flows through them one after another. The
circuit above shows three resistors (R1,R2,R 3)
connected in series and the direction of current (I) is indicated with an arrow
to show the direction of flow of current through the circuit when a source
voltage (E) is applied.
connected in series when current flows through them one after another. The
circuit above shows three resistors (R1,R2,R 3)
connected in series and the direction of current (I) is indicated with an arrow
to show the direction of flow of current through the circuit when a source
voltage (E) is applied.
Since, the current
has only one path to travel, the current flowing through each of the resistors
is the same.
has only one path to travel, the current flowing through each of the resistors
is the same.
I = I1 = I2
= I3 – – – – – – (1)
= I3 – – – – – – (1)
Where I is the total
current flowing through the circuit and I1,I2,I3
are the currents flowing through resistors R1, R2 and R3
respectively.
current flowing through the circuit and I1,I2,I3
are the currents flowing through resistors R1, R2 and R3
respectively.
The sum of the
voltage drops at R1,R2,R3 is equal to the
total voltage supplied by the source voltage (or battery).
voltage drops at R1,R2,R3 is equal to the
total voltage supplied by the source voltage (or battery).
V = V1 + V2
+ V3 – – – – – (2)
+ V3 – – – – – (2)
Where V is the
applied voltage (or total circuit voltage) and V1, V2 and
V3 are the voltage drops across R1, R2, R3
respectively.
applied voltage (or total circuit voltage) and V1, V2 and
V3 are the voltage drops across R1, R2, R3
respectively.
Since V = IR (Ohm’s
Law)
Law)
Then V = I1R1
+ I2R2 + I3R3 – – – – (3)
+ I2R2 + I3R3 – – – – (3)
To satisfy Ohm’s law
for the entire circuit
for the entire circuit
V = IRequivalent – – – – – – (4)
Equating (3) and (4),
we get
we get
IRequivalent
= I1R1 + I2R2 + I3R3 – – – (5)
= I1R1 + I2R2 + I3R3 – – – (5)
Since the current through
each of the resistors is equal to the total current, I – I1, I2,
and I3 can be represented by I
each of the resistors is equal to the total current, I – I1, I2,
and I3 can be represented by I
IRequivalent =
I (R1 + R2 + R3) – – – – (6)
I (R1 + R2 + R3) – – – – (6)
By cancelling I from
both sides of (6), we arrive at the expression for equivalent resistance for
resistors connected in series
both sides of (6), we arrive at the expression for equivalent resistance for
resistors connected in series
Requivalent =
R1 + R2 + R3 – – – – (7)
R1 + R2 + R3 – – – – (7)
In general, the
equivalent resistance of resistors connected in series is the sum of their
resistance, that is
equivalent resistance of resistors connected in series is the sum of their
resistance, that is
Requivalent
= ∑Rl – – – – – – (8)
= ∑Rl – – – – – – (8)
The circuit above
shows three resistors connected in a circuit with an applied voltage of 10V.
Calculate the equivalent resistance of the circuit.
shows three resistors connected in a circuit with an applied voltage of 10V.
Calculate the equivalent resistance of the circuit.
Solution
Requivalent
= R1 + R2 + R3
= R1 + R2 + R3
Where R1, R2
and R3 represents 5KΩ, 7KΩ and 1KΩ respectively.
and R3 represents 5KΩ, 7KΩ and 1KΩ respectively.
Requivalent
= 5 + 7 + 1
= 5 + 7 + 1
= 13KΩ
