1. Chapter 20
Circuits
And
Circuit Elements

2. 20.1 Schematic Diagrams and Circuits
Objectives
Interpret and construct circuit diagrams
2. Identify circuits as open or closed
3. Deduce the potential difference across a
circuit load, given the potential difference
across the battery’s terminals

3. Schematic Diagram …is a graphic representation of an
electric circuit, with standardized
symbols representing circuit
components (aka, circuit diagram)

4. Circuit Elements and Symbols

5. Draw the schematic for this circuit

6. Interpret the circuit elements in this schematic

7. Electric Circuit …a set of electrical components
connected so that they provide
one or more complete paths for
the movement of charges (i.e.,
paths for current to flow)

8. Circuit Definitions Load – any element or group of elements
in a circuit that dissipates energy
Open circuit – incomplete path in a circuit,
resulting in no current flow
Closed circuit – a closed loop path exits
in which current can flow
Short circuit – a circuit without a load, so
there is very little (essentially
none) resistance to current

9. A couple more definitions….
emf – the energy per unit charge supplied
by a source of electric current. Any
device that increases the potential
energy of the charges in a circuit is
a source of emf.
Battery terminal voltage – is slightly less
than emf due to the battery’s internal
resistance (from charges colliding with
atoms as they move from one terminal
to the other inside the battery)

10. emf versus terminal voltage
The emf () is the “ideal”
voltage available from
the battery. The terminal
voltage (Vt) is the actual
maximum voltage available
from the battery, which is
Slightly less than emf due to
the internal resistance (r) of
the battery.

11. Conservation of Energy in a Circuit
Inside the battery – the chemical energy of the battery
is converted to electrical potential energy of the charge
Outside the battery – the charge’s electrical potential
energy is converted to other forms of energy (light, heat)
Conservation of energy – the charge must gain as much
as it loses in one complete trip around the circuit

12. 20.2 Resistors in Series or in Parallel
Objectives
Calculate the equivalent resistance (Req) for a circuit of resistors in series, and find the current and potential difference across
each resistor in the circuit.
2. Calculate the equivalent resistance (Req) for a circuit of resistors in parallel, and find the current and potential difference across each resistor in the circuit.

13. Series vs Parallel Series – describes a circuit or portion of
a circuit that provides a single
conducting path without junctions
Parallel – describes two or more components
in a circuit that are connected
across common points or junctions,
providing separate conducting
paths for the current

14. Series Circuit
Parallel Circuit

15. Calculations for Resistors in Series
Resistors in series all have the same current
running through them
ΔVt = ΔV1 + ΔV2 + ΔV3….
and ΔV = IR
but I is the same
everywhere
So, IReq = IR1 + IR2 + IR3…
So, IReq = I(R1 + R2 + R3)….
which becomes
Req = R1 + R2 + R3…

16. Calculations for Resistors in Parallel
Resistors in parallel all have the same potential difference across them
It = I1 + I2 + I3…
But ΔV is the same everywhere, so…

17. Facts: Series vs Parallel Resistors
Req for resistors in series is always greater than any individual resistance in the circuit
Req for resistors in parallel is always less than the smallest resistance in the circuit
Series circuits require all elements to conduct
Parallel circuits do not require all elements to conduct

18. SERIES PARALLEL Req = R1 + R2 + R3 + … 1/Req = 1/R1 + 1/R2 + 1/R3 + …
I is constant around the circuit, so I is the same at each resistor
It = IR1 = IR2 = IR3
I across each resistor is different (assuming different R’s) and the total current is
It = IR1 + IR2 + IR3 + …
ΔV is different across each resistor (assuming different R’s) and the total potential difference is
ΔVtotal = VR1+VR2+VR3+… = ΔVsource
ΔV is the same across each resistor
Vsource =VR1=VR2=VR3

19. Questions A 9.0V battery is connected in series to four
light bulbs having resistances of 2.0Ω, 4.0Ω,
5.0Ω and 7.0Ω.
a) Draw circuit
b) What is Req ?
c) What is I?
2. The same light bulbs from problem #1 are now
connected in parallel to the 9.0V battery.
a) Draw circuit
b) What is Req?
c) What is I?

21. Answers
a) Req = 18.0 Ω
b) I = 0.50 A
2. a) Req = Ω
b) I = 9.8 A

22. 20.3 Complex Resistor Combinations
Objectives
Calculate the equivalent resistance for a
complex circuit involving both series and
parallel portions
Calculate the current in and the potential
difference across individual elements
within a complex circuit

23. Combination of some resistors in series and some resistors in parallel
Complex Circuits
Combination of some resistors in series
and some resistors in parallel

24. Calculating Req and I for a Complex Circuit
What is Req for this circuit?
What is I?

25. Answers
Req = 60 Ω
I = 2 A

26. What is I at R4? What is ΔV across R4?
Calculating I and ΔV Across an Individual Resistor in a Complex Circuit
What is I at R4?
What is ΔV across R4?

27. Answers
I at R4 = 1.5 A
ΔV across R4 = 22.5 V

28. Complex Circuit Example
Req = ?
It = ?
c) V across 2.0 resistor = ?
d) I in 4.0 resistor = ?

29. Solving Complex Circuits with Kirchoff’s Rules
The sum of the currents entering any
junction must equal the sum of the
currents leaving that junction.
The sum of the potential differences (ΔV’s)
around any closed circuit loop must be zero.

30. Kirchoff’s Rules Approach
1. Choose a junction and draw your current
arrows in and out of the junction
2. Choose your voltage loops (need to use 1 less
loop than the total number of loops), and
choose the direction of current flow in each loop
3. Write out your junction and loop equations in
terms of current.
4. Solve for the unknown currents in all equations
If any or your currents end up negative, then
their direction is opposite of what you chose

31. Adding or Subtracting in the Voltage Loops for Kirchoff’s Rules
Choose a loop direction
2. If you cross the battery from negative to positive then you gain energy so ADD ΔV
3. If you cross the battery from positive to negative
then you lose energy so SUBTRACT ΔV
4. If your loop direction is the same as the current
direction as you cross a resistor then SUBTRACT IR
5. If your loop direction is opposite the current
direction as you cross a resistor then ADD IR

33. Use Kirchoff’s Rules Let’s use this junction for Rule #1
Let’s use these 2 loops for Rule #2

34. Measuring Resistance (R)
To measure resistance, the resistor must not be attached to an active circuit (i.e., no current can be flowing through
the resistor).
On the meter, the black plug goes to COM, the red plug
goes to  and the dial must be set to . Sometimes there
are multiple scales for . Choose the appropriate scale to
provide the most precise resistance measurement.

35. Measuring Current (I) To measure current, the
current must flow through
the meter, therefore the
meter has to be connected
in series in the circuit.
On the meter, the black
plug goes to COM, the
red plug goes to mA or A
and the dial must be set to
mA or A scale.

36. Measuring Voltage (V)
To measure V (also known
as “voltage drop”) across a
circuit load, the meter has to
be connected in parallel
with the load.
On the meter, the black
plug goes to COM, the
red plug goes to V and the
dial must be set to DC volts
scale (if using a battery circuit).