Electrical Circuits and
Circuit Diagrams
Bellwork: Use the Ohm's law equation to determine
the missing values in the following circuits.
Drawing Electrical Circuit
Diagrams
Commonly Used Symbols for DC
Circuits
name
variable
unit
source of emf
ε
volts V
Resistor
R
ohms Ω
wires
n/a
n/a
switch
n/a
n/a
Ammeter
I
amperes A
voltmeter
U orV
volts V
symbol
1. A current is said to exist
whenever _____.
a. a wire is charged
b. a battery is present
c. electric charges are unbalanced
d. electric charges move in a loop
2. Current has a direction. By
convention, current is in the
direction which ___.
a. + charges move
b. - electrons move
c. + electrons move
3. If an electric circuit could be
compared to a water circuit at a
water park, then the current would
be analogous to the ____.
A. water pressure
B. gallons of water
flowing down slide
per minute
C. water
D. bottom of the slide
E. water pump
F. top of the slide
5. The diagram at the right depicts a
conducting wire. Two cross-sectional
areas are located 50 cm apart. Every 2.0
seconds, 10 C of charge flow through
each of these areas. The current in this
wire is ____ A.
a. 0.10
b. 0.25
c. 0.50
d. 1.0
e. 5.0
f. 20
g. 10
h. 40
6. Use the diagram at the right to
complete the following statements:
a. A current of one ampere is a flow of
charge at the rate of _______ coulomb per
second.
b. When a charge of 8 C flows past any
point along a circuit in 2 seconds, the
current is _____ A.
c. If 5 C of charge flow past point A
in 10 seconds, then the current is___ A.
d. If the current at point D is 2.0 A, then
___ C of charge flow past point D in
10 seconds.
e. If 12 C of charge flow past point A in
3 seconds, then 8 C of charge will flow
past point E in ________ seconds.
True or False: The current at point
E is considerably less than the
current at point A since charge is
being used up in the light bulbs.
Power
• Power: the rate at which work is done or energy
is used
Power = Work/time or Power = Energy/time
• Measured in watts
1 watt = 1 J/sec
• Power is CONSERVED in circuits; that is, the
power supplied by the battery must be equal to
the power consumed by all of the resistors in the
circuit.
• Joule’s Law: P = IV
• Combined with Ohm’s Law: P = I2R = V2/R
Example Problems
1. Which would be thicker (wider) - the filament of a 60Watt light bulb or the filament of a 100-W light bulb?
Explain.
2. Calculate the resistance and the current of a 7.5-Watt
night light bulb plugged into a US household outlet
(120 V).
3. Calculate the resistance and the current of a 1500-Watt
electric hair dryer plugged into a US household outlet
(120 V).
4. The box on a table saw indicates that the amperage at
startup is 15 Amps. Determine the resistance and the
power of the motor during this time.
More Power Problems
5. The sticker on a compact disc player says that it
draws 288 mA of current when powered by a 9
Volt battery. What is the power (in Watts) of the
CD player?
6. A 541-Watt toaster is connected to a 120-V
household outlet. What is the resistance (in ohms)
of the toaster?
7. A color TV has a current of 1.99 Amps when
connected to a 120-Volt household circuit. What is
the resistance (in ohms) of the TV set?
Electricity in Series
Electricity In Series Circuits
• The current must be the same through all
resistors when the resistors are in series
Req = R1 + R2 + R3
Veq = V1 + V2 + V3
Ieq = I1 = I2 = I3
Example Problems
8. What would be the equivalent resistance
of the resistors shown above?
9. When the 2A current flows through the
resistors, what total voltage will be lost
across this combination?
10.How much power is dissipated by these
resistors?
Electricity in Parallel
Electricity in Parallel Circuits
• When resistors are connected in parallel, the
voltage drop across each resistor is the same. The
current divides among the resistors. It divides
proportionally with the larger ratio going along
the "path of least resistance."
• I =V/R
Ieq = I1 + I2 + I3
• I = V/R1+V/R2+V/R3 …
• =V(1/R1 + 1/R2 + 1/R3 …)
Example Problems
15.
16.
17.
18.
19.
20.
If R1 = 6 Ω and R2 = 6 Ω, how much current flows
through each resistor?
If R1 = 6 Ω and R2 = 12 Ω, how much current flows
through each resistor now?
If R1 = 18 Ω and R2 = 6 Ω, how much current flows
through each resistor?
What is their equivalent resistance?
What is the total voltage lost between points X and Y?
How much current flows through each resistor in the
circuit shown above?
Practice – Resistors in Series and
Parallel Circuits Mini-Lab
• Log on to the PhET website and select the DC
Circuit Construction Kit.
• http://phet.colorado.edu/simulations/sims.
php?sim=Circuit_Construction_Kit_DC_Onl
y
• Answer the questions in your instruction
sheet as you go. Make sure you accomplish
all experiments requiring real lab equipment
BEFORE you leave class today!
• Electrical Circuits Quiz Friday 03/20/09
WarmUp
A color TV has a current of 1.99
Amps when connected to a 120Volt household circuit. What is
the resistance (in ohms) of the
TV set?
Combinations of Circuits
Series Circuits
• The current is the same in every resistor;
this current is equal to that in the battery.
• The sum of the voltage drops across the individual
resistors is equal to the voltage rating of the battery.
• The overall resistance of the collection of resistors is
equal to the sum of the individual resistance values,
• Rtot = R1 + R2 + R3 + ...
• Parallel Circuits
• The voltage drop is the same across each parallel branch.
• The sum of the current in each individual branch is equal
to the current outside the branches.
• The equivalent or overall resistance of the collection of
resistors is given by the equation 1/Req = 1/R1+1/R2+1/R3
Simplifying a Circuit Diagram
Problem Solving Strategy
1. If a schematic diagram is not provided, take the
time to construct one.
2. Take the time to organize yourself, writing down
known values and equating them with a symbol
such as Itot, I1, R3, V2, etc.
3. Know and use the appropriate formulas for the
equivalent resistance of series-connected and
parallel-connected resistors.
4. Simply the circuit into a series circuit by replacing
the parallel section with a single resistor.
5. Use the Ohm's law equation (V = I • R) often and
appropriately.
Evaluating Combination Circuits
• Use Ohm’s Law to simplify the circuit
Example Problem 15
Solution to Problem 15
Example Problem 16
Solution to Problem 16
Complete the following Chart