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Circuits
AP Physics 1
A Basic Circuit
 All electric circuits have three
main parts
 A source of energy
 A closed path
 A device which uses the
energy
 If any part of the circuit is open
the device will not work!
Potential Difference
 In a battery, a series of chemical reactions
occur in which electrons are transferred
from one terminal to another. There is a
potential difference (voltage) between
these poles.
 The maximum potential difference a
power source can have is called the
electromotive force or (EMF), ε. The term
isn't actually a force, simply the amount
of energy per charge (J/C or V).
 The unit for potential difference is volt
(V).
Current
 If Q is the total amount of charge that has moved past a point in a wire,
we define the current I in the wire to be the rate of charge flow:
𝐼=
∆𝑄
∆𝑡
 Current is the rate at which charge
flows
 The SI unit for current is the coulomb
per second, which is called the
ampere.
 1 ampere = 1 A = 1 C/s.
 Conventional current flow is the flow
of positive charge.
Modeling Current
 When a voltage is applied to a circuit, there is an electric field present
inside the wire.
 This field causes electrons to move through the wire.
 The electrons frequently collide with positive charges, which causes
them to drift through the wire very slowly.
Resistance
 Resistance (R) is defined as
the restriction of electron
flow.
 Each time charges collide
with nuclei, some of their
kinetic energy is converted
into thermal energy.
 The unit for resistance is
Ohm (Ω).
Ohm’s Law
 For most materials, increasing
the amount of voltage increases
the current through the
material.
 Our constant of proportionality
between these two values is the
resistance of the material.
 This formula is referred to as
Ohm’s Law.
Electrical Power
 When current runs through a lightbulb or a resistor, it dissipates
electrical energy into heat.
 The dissipated electrical power can be calculated using one of the
following equations:
 The unit for power is a watt (W), just like in mechanics.
Basic Circuit Components
 Before you begin to understand circuits you need to be able to draw what
they look like using a set of standard symbols understood anywhere in the
world
 For the battery symbol, the long
line is considered to be the positive
terminal and the short line,
negative.
 The voltmeter and ammeter are
special devices you place in or
around the circuit to measure the
voltage and current.
Using a Voltmeter and Ammeter
 The voltmeter and ammeter cannot
be just placed anywhere in the
circuit. They must be used according
to their definition.
 Since a voltmeter measures voltage
or potential difference it must be
placed across the device you want to
measure. That way you can measure
the change on either side of the
device.
 Since the ammeter measures the
current or flow it must be placed in
such a way as the charges go through
the device.
Ways to Wire Circuits
 There are 2 basic ways to wire a circuit. Keep in mind that a resistor
could be anything (bulb, toaster, ceramic material…etc)
 Series – One after another
 Parallel – between a set of junctions and parallel to each other
Strategy For Solving Circuits
 Circuit problems will often give you a battery and various resistors. The resistors
will be in series, parallel, or a combination of the two.
 The goal is generally to calculate the total resistance, which essentially turns all
of your resistors into one resistor.
 With one battery and one resistor, you can use Ohm’s Law to calculate the total
current in the circuit. By knowing this total current, the battery voltage, and the
resistance of each resistor, you can calculate voltage across resistors and current
through resistors.
Series Circuit
 In a series circuit, the
resistors are wired one after
another. Since they are all
part of the same loop they
each experience the same
amount of current.
 The sum of the voltages
across each resistor is equal
to the total voltage of the
battery.
I ( series)Total  I1  I 2  I 3
V( series)Total  V1  V2  V3
Equivalent Resistance in Series
 As the current goes through the
circuit, the charges must use
energy to get through the resistor.
 Each individual resistor will eat up
some electric potential. We call
this voltage drop.
V( series)Total  V1  V2  V3 ; V  IR
( I T RT ) series  I1 R1  I 2 R2  I 3 R3
Rseries  R1  R2  R3
Rs   Ri
Example
A series circuit is shown to the left.
a) What is the total resistance?
R(series) = 1 + 2 + 3 = 6W
b) What is the total current?
V=IR
12=I(6)
I = 2A
c) What is the current across EACH
resistor?
They EACH get 2 amps!
d) What is the voltage drop across
each resistor?( Apply Ohm's law to
each resistor separately)
V1W(2)(1) 2 V
V3W=(2)(3)= 6V
V2W=(2)(2)= 4V
Notice that the individual VOLTAGE DROPS add up to the TOTAL!!
Example
Calculate the equivalent resistance of
the circuit, the current in the circuit,
and the voltage drop across each
resistor.
Parallel Circuit
 In a parallel circuit, we have
multiple loops. So the current
splits up among the loops
with the individual loop
currents adding to the total
current.
 It is important to understand
that parallel circuits will all
have some position where
the current splits and comes
back together. We call these
junctions.
 The current going in to a
junction will always equal the
current going out of a
junction.
I ( parallel)Total  I1  I 2  I 3
Regarding Junctions :
I IN  I OUT
Equivalent Resistance in Parallel
 Notice that the junctions both touch the
positive and negative terminals of the
battery. That means you have the same
potential difference down each individual
branch of the parallel circuit. This means
that the individual voltages drops are equal.
V( parallel)Total  V1  V2  V3
I ( parallel)Total  I1  I 2  I 3 ; V  IR
VT
V1 V2 V3
( ) Parallel  

RT
R1 R2 R3
1
1
1
1
 

RP R1 R2 R3
1
1

RP
Ri
Example
To the left is an example of a parallel circuit.
a) What is the total resistance?
1 1 1 1
  
RP 5 7 9
1
1
 0.454  RP 
 2.20 W
Rp
0.454
V  IR
b) What is the total current?
8  I ( R )  3.64 A
V  IR
8
I 5W   1.6 A
5
c) What is the voltage across EACH resistor?
8 V each!
d) What is the current drop across each resistor?
(Apply Ohm's law to each resistor separately)
I 7W 
8 1.14 A
8

I 9W   0.90 A
7
9
Notice that the
individual currents
ADD to the total.
Example
Calculate the equivalent resistance of the circuit, the current in
each resistor, and the voltage drop across each resistor.
Complex Circuits
 Combinations of resistors can often be reduced to a single equivalent
resistance through a step-by-step application of the series and parallel
rules.
 Once you have found the total resistance of the circuit, you can
determine the total current in the circuit. That current can be used to
calculate the voltage drop across each resistor.
Compound (Complex) Circuits
Many times you will have series and parallel in the SAME circuit.
Solve this type of circuit from
the inside out.
WHAT IS THE TOTAL
RESISTANCE?
1
1
1

 ; RP  33.3W
RP 100 50
Rs  80  33.3  113.3W
Compound (Complex) Circuits
1
1
1

 ; RP  33.3W
RP 100 50
Rs  80  33.3  113.3W
Suppose the potential difference (voltage) is equal to 120V. What is the total
current?
VT  I T RT
120  I T (113.3)
I T  1.06 A
What is the VOLTAGE DROP across the 80W resistor?
V80W  I 80W R80W
V80W  (1.06)(80)
V80W 
84.8 V
Compound (Complex) Circuits
RT  113.3W
VT  120V
I T  1.06 A
V80W  84.8V
I 80W  1.06 A
What is the VOLTAGE DROP across the
100W and 50W resistor?
VT ( parallel)  V2  V3
VT ( series)  V1  V2&3
120  84.8  V2&3
V2&3  35.2 V Each!
What is the current across the 100W
and 50W resistor?
I T ( parallel)  I 2  I 3
I T ( series)  I1  I 2&3
35.2
I100W 

100
35.2
I 50W 

50
0.352 A
Add to
1.06A
0.704 A
Kirchhoff’s Voltage Law (KVL)
 Kirchhoff’s voltage law states that if you travel along any closed loop, the sum
of the potential differences will be zero.
 Each element in the loop (battery, resistor, etc.) creates a potential difference;
sometimes they will be a rise in potential, sometimes they will be a drop in
potential.
Kirchhoff’s Current Law (KCL)
 Kirchhoff’s Current Law states
that the current flowing into a
junction is equal to the sum the
currents flowing out.
åI = åI
in
out
 You can think of the current as
water and the wires as pipes. If
water is in one pipe and
encounters two pipes, some of the
water will go into one and the rest
will go into the other. The
important idea is that we are not
gaining or loosing any water, but
simply redirecting it.
Example
There is a current of 1.0 A in the
following circuit. What is the resistance
of the unknown circuit element?
The diagram below shows a
segment of a circuit. What is the
current in the 200 Ω resistor?
Internal Resistance
 All components in a circuit
offer some type of resistance
regardless of how large or
small it is.
 Real batteries have what is
called an internal resistance.
This can be modeled as an
additional resistor in series
with the battery.
Example
Suppose we have a car battery with an emf = 13.8 V, under a resistive
load of 20 Ω ,the voltage sags to 11.8 V.
a) What is the battery's resistance?
b) What is the rate at which energy is dissipated in the battery?
Resistivity and Conductivity
 All wires exhibit some amount of resistance, and it is dependent primarily on
the geometry and the resistivity (a material property) of the wire.
 In many circuits we can consider the wire to be of negligible resistance, but
we can calculate the resistance nonetheless.
 The resistance of a material is the inverse of the material’s conductivity.
𝜌 = 𝑅𝑒𝑠𝑖𝑠𝑡𝑖𝑣𝑖𝑡𝑦
𝜎 = 𝐶𝑜𝑛𝑑𝑢𝑐𝑡𝑖𝑣𝑖𝑡𝑦
𝜌𝑙
𝑅=
𝐴
1
𝜌=
𝜎
Example
Calculate the resistance of a one meter length of 24 SWG Nichrome wire.
SWG  Standard Wire Gauge
24 SWG  0.558mm in diameter
 Nichrome  1.10 x106 Wm
As you can see, using significant amounts of wire can greatly influence the
voltage drops, current, and power produced in circuits.