Download resistance_in_series_and_parallel

True or False?
• The electrons in a circuit move in the
same direction as the current.
• The current through a component is
directly proportional to the voltage if
the resistance of the component
stays the same.
• The resistance in a wire is directly to
the thickness of the wire.
True or False?
• In a filament lamp the resistance
increases with the voltage.
• The electrons lose part of the E.M.F.
provided by the battery as they go
around the circuit once.
• In a thermistor the resistance is
higher when the weather is cooler.
Resistance in Series and
Parallel
• Resistance in series circuits
• Resistance in parallel circuits
Resistance in series circuits
Use Ohm’s law to calculate the voltage
across the resistors in the next slide.
Write your values in the voltmeters and see
if they agree with the actual readings.
.603
Amps
2.2 Ω
1.5 Ω
.897
1.332
Volts
Volts
What should the
voltage across the
two resistors be?
.601
Amps
2.2 Ω
1.5 Ω
2.231
Volts
Equivalent resistance
The two resistors in the previous series
circuit can be thought of as a single resistor.
Work out and write the equivalent
resistance using Ohm’s law and the values
of current and voltage shown.
2.231 V
3.7 Ω
0.601 A
Equivalent resistance
In a series circuit the total resistance of the
components is the sum of the resistance of each
component. So, the equivalent resistance R is found
as:
R = R1 + R2
R1
R2
R
2.2 Ω
1.5 Ω
3.7 Ω
Resistance in parallel circuits
Look at the parallel circuit on the next slide
and work out the current in the main circuit
and through each resistor in the parallel
branches.
What do you think
the current in the
main circuit should
be?
1.830
1.991
Volts
Amps
2.2 Ω
0.832 A
1.716
Volts
1.144 A
1.5 Ω
Resistance in parallel circuits
The current in the
main circuit is the
sum of the currents
in the parallel
branches:
I
I1
R1
I2
R2
I = I 1 + I2
Work out the
combined resistance
in the main circuit
with these values of
current and voltage
1.830
1.991
Volts
Amps
2.2 Ω
1.716
Volts
1.5 Ω
Combined resistance
Using the values of V and
I in the previous slide
and Ohm’s law to work
out the combined
resistance, we find:
I
I1
R1=2.2 Ω
I2
R2=1.5 Ω
V
1.8 V
R= =
= 0.9 Ω
I 1.99 A
What can you notice about the combined resistance?
Combined resistance
The combined resistance R = 0.9 Ω is less than
R1 = 2.2 Ω or R2 = 1.5 Ω. You can work out
the combined resistance of a parallel circuit
using these formulae:
1 1 1
 
R R1 R2
or
R1  R2
R
R1  R2
What is the combined resistance when the resistors are the
same?
What is the equivalent circuit?
8A
8A
80VV
32 W
32 W
30VV
2.5 A
2.5 A
V
V
12 W
12 W
Whatis
Split
This
the
isathe
branches
series
equivalent
circuit
in two
where
circuit?
separate
the current
circuits.
is 2.5
What
A (the
is this
reading
circuit?the branch). What is the voltage across the two
inside
A
W
W
A
resistors?
V=RxI
What is the equivalent circuit?
Now you can deal with this. What is the voltage, current and
resistance?
8A
8A
80VV
32 W
32 W
110
2.5 A
2.5
A
44 W
30VV
12 W
12 W
110VV
What is the equivalent resistance and the voltage across?
W
20 W
A
5.5 A