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Lesson 6
SERIES AND PARALLEL
CIRCUITS
Lesson 6: Equivalent Resistance of Circuits
AP Physics B Objectives
III.C.2. Steady State DC circuits with batteries and resistors
2. Steady-state direct current circuits with batteries and resistors only
a) Students should understand the behavior of series and parallel
combinations of resistors, so they can:
(1) Identify on a circuit diagram whether resistors are in series or in parallel.
(2) Determine the ratio of the voltages across resistors connected in series
or the ratio of the currents through resistors connected in parallel.
(3) Calculate the equivalent resistance of a network of resistors that can be
broken down into series and parallel combinations.
Student Objectives
Students will be able to:
1. Determine the equivalent resistance of series and parallel
combinations of resistors.
2. Determine the voltage drop and/or current through a series or
parallel circuit.
3. Construct series and parallel combinations of resistors.
Announcements
Current HW #5 & 6 due TUESDAY
Modern HW #5 due TUESDAY
HW QUIZ on TUESDAY 
Lunch labs will be ONLINE this week
Fluids & Thermo packet due Thurs, March 28
Electricity packet due Mon, April 8
Modern, Optics, Waves packet due Wed, April 10
Series arrangement of
components
Series components are put together so
that all the current must go through
each one
I
Three bulbs in series all have
the same current.
Parallel arrangement of
components
Parallel components are put together so
that the current divides, and each
component gets only a fraction of it.
1/3 I
I
1/3 I
1/3 I
1/3 I
I
1/3 I
1/3 I
Three bulbs in parallel
Voltmeter
A voltmeter measures the drop in
electric potential, or voltage, between
any two points in a circuit.
Voltmeters are always connected in
parallel with the circuit.
MiniLab #5
Draw a circuit containing two cells in series, two bulbs
in series, and a switch.
Wire these together.
a) What changes in the circuit when you unscrew one of the
bulbs?
b) Measure the voltage across the battery and across each bulb.
How does the voltage of the batteries compare to the voltage
across each bulb?
MiniLab #6
Draw a circuit containing two cells in series, two
bulbs in parallel, and a switch.
Wire this on your circuit board.
a) What do you observe happens to the bulbs when you
unscrew one bulb?
b) Measure the voltage across the battery and across each
bulb. What do you observe?
Data Analysis
Series
Parallel
Current
Same through each bulb
Splits at junction
Voltage
Divides
Same through each
Power
Dimmer than parallel
Brighter than series
Remove a bulb All lamps go out
Only the removed bulb goes
out; others shine at same
intensity
Terminal Voltage and EMF
A real battery is then modeled as if it were a perfect
emf E in series with a resistor r.
Terminal voltage Vab is measured by meter connected
in parallel
When no current is drawn from the battery, the
terminal voltage equals the emf.
When a current I flows from the battery, there is an
internal drop in voltage equal to Ir, thus the terminal
voltage (actual voltage delivered) is Vab = E - Ir