Transcript SPH3U - K-Moncrief

SPH3U: Electricity
Kirchhoff's Laws & Resistors
Circuits
Review
 Label the following as a Parallel Circuit or
a Series Circuit. Label all the parts of each
circuit.
V
+
-
+
A
-
Loads
 Any component or device in a circuit that
transforms electric potential energy into some
other form of energy, causing an electric
potential drop, is called a load. Two loads in
the above diagrams are: the light bulb and
the resistor.
Series and Parallel Circuits

To understand how series circuits and parallel
circuits work, we need to answer two
questions:
1. When electrons have several loads to
pass through, what controls the amount of
electric potential energy they will lose at
each load?
2. When electrons can follow several
possible paths, what controls the number
of charges that will take each path?
Series and Parallel Circuits

To answer these questions, we need to talk
about two important laws for electric circuits:
Law of Conservation of Energy

As electrons move through an electric circuit
they gain energy in sources and lose energy in
loads, but the total energy gained in one trip
through a circuit is equal to the total
energy lost.
Law of Conservation of Charge

Electric charge is neither created nor lost in
an electric circuit, nor does it accumulate at
any point in the circuit.
Kirchhoff's Laws

A German physicist, Gustav Robert Kirchhoff
(1824 -1887) performed experiments and was
able to describe these conservation laws as
they apply to electric circuits:
Kirchhoff's Laws

Kirchhoff's Voltage Law (KVL)
Around any complete path through an electric
circuit, the sum of the increases in electric
potential is equal to the sum of the decreases
in electric potential.
Vtotal = V1 + V2 + V3 + … + Vn
(in a series circuit)
Vtotal = V1 = V2 = V3 = … = Vn
(in a parallel circuit)
Kirchhoff's Laws

Kirchhoff's Current Law (KCL)
At any junction point in an electric circuit, the
total electric current into the junction is equal
to the total electric current out.
Itotal = I1 = I2 = I3 =…= In
(in a series circuit)
Itotal = I1 + I2 + I3 +…+ In
(in a parallel circuit)
Kirchhoff's Laws

These relationships are very important to
understand the transfer of electrical energy in
a circuit. They provide the basis for electric
circuit analysis in this course.
Example Problem 1

Calculate the potential difference, V2, in
the circuit shown in the figure below.
Example Problem 1

Calculate the potential difference, V2, in
the circuit shown in the figure below.
Example Problem 2

Calculate the electric current, I3, in the
circuit shown in the figure below.
Example Problem 2

Calculate the electric current, I3, in the
circuit shown in the figure below.
Since this is a
parallel circuit,
Itotal = I1+I2 +I3
Therefore, I3 = 6A
Resistance

When charges pass through a material or
device, they experience an opposition or
resistance to their flow.

Remember: Current is the number of
electrons moving in the same direction
past a certain point in one second. The
symbol for electric current is I.
Resistance

Increasing the resistance in a circuit
decreases the current that flows.

In 1827 a man named Georg Simon Ohm
discovered that current and the potential
difference V are directly proportional.
Resistance

This means I α V  The more current you
have (the more coulombs per second going
past a point), the greater the electrical
energy.

This is summarized as OHM’s LAW  The
potential difference V across a conductor
is directly proportional to the current that
flows in the conductor.
Resistance

We can also write this as an equation if we put
in a constant.

V = cR, where c is a constant
 But this property depends on the
resistance… so we will make the constant
c = R, and define R as the resistance.
Ohm’s Law

V = IR or V  R
I
Ohm’s Law
Note: V is measured in volts
I is measured in amperes.
…. So R is measured in: volts ampere  OHMs  
1 Ω is the electric resistance of a conductor
that has a current of 1 A through it when the
potential difference across it is 1 V.
 1 Ω = 1 V/A

Example Problem 3

What is the potential difference across a
toaster of resistance 13.8 Ω when the
current through it is 8.7 A?
Example Problem 3

What is the potential difference across a
toaster of resistance 13.8 Ω when the current
through it is 8.7 A?
Resistors in Series

Resistors are put in many electronic
machines to reduce the current and protect the
machine parts.
Equivalent Resistors

Look at the
diagram. It
shows a circuit
with three
resistors
connected in
series.
R3 = 10 Ω
+
-
R1 = 6 Ω
R2 = 5 Ω
Equivalent Resistors

We would like to find the equivalent resistor
 We would like to take out all the
resistors and put in just one ‘superresistor’ that would make the circuit
behave in the exact same way.

Remember from Kirchhoff's Law:
Vtotal = V1 + V2 + V3 + ….
Equivalent Resistors

Use Ohm’s Law to substitute V = IR:
 ItotalRtotal
= I1R1 + I2R2 + ….
Equivalent Resistors

But we also know from Kirchhoff's law that for
a series circuit Itotal = I1 = I2 = I3 = ……

So, we get ItotalRtotal = Itotal (R1 + R2 + R3 +…)

Therefore, Rtotal = (R1 + R2 + R3 + …)

This means, looking back at our original
question, that the equivalent resistor to the
diagram is R1 + R2 + R3 = (6 + 5 + 10) Ω =
21Ω
Example Problem 4

What is the equivalent resistor in a series
circuit containing a 16 Ω light bulb, a 27Ω
heater, and a 12 Ω motor?
Example Problem 4

What is the equivalent resistor in a series
circuit containing a 16 Ω light bulb, a 27Ω
heater, and a 12 Ω motor?
Resistance in Parallel

We can use the same approach to find the
equivalent resistance of several resistors
connected in parallel.

Remember from Kirchhoff's Law:
Itotal = I1 + I2 + I3+…
Resistance in Parallel

Use Ohm’s Law to substitute I = V/R:
Vtotal V1 V2 V3



 ...
Rtotal R1 R2 R3

But we also know from Kirchhoff’s law that for
a parallel circuit
Vtotal = V1 = V2 = V3 = …
Resistance in Parallel


So, we get
Therefore,
Vtotal
Vtotal

Rtotal ( R1  R2  R3  ...)
1
1

Rtotal ( R1  R2  R3  ...)
Homework
Read sections 11.6 & 11.7 in your text.
 Complete the following questions:

Pg. 522 # 1-2
 Pg. 526 # 2, 4, 6.
 Pg. 530 # 5 (a-d)
