1
DC circuits, Kirchhoﬀ
`
s Laws
CHM6158C ‐ Lecture
2
•
Alternating Current (AC), Direct Current (DC)
•
DC Circuits
•
Resistors
•
Kirchhoff
`
s Laws
2
Electric current
Movement of electrons in a conductor
Examples of good conductors:
•
copper
•
aluminum
•
silver
Cable enclosed with an insulating
material (e.g. polyethylene)
http://www.hydroquebec.com/learning/images/quest
ceque/i_schema_atome.gif
Units
:
Charge (Q)
Coulomb (C)
1.603x10
19
C
Voltage (V)
Volts (V)
1 V = 1 J/C
Current (I)
Amperes (A)
1 C/s
Power (P)
Watts (W)
P = IV
At what speed does
electricity propagate?
A current of 100 mA can be lethal !
3
Conduc@vity
Conductivity = measure of a material
`
s ability to conduct an electrical current
Inverse: Resis@vity vs. Resistance
silver > copper > aluminum
Resistivity
= measure of how strongly a material opposes the flow of electrical
current (units:
Ω
m) (inherent of material)
J
E
ρ
Magnitude of electric field (V / m)
Magnitude of current density (A / m
2
)
Resistance
= measure of how strongly a material opposes the flow of electrical
current (units:
Ω
) (dependent on crosssection and length of material)
I
V
R
OHM
`
s LAW
Strange units –
why?
4
Alterna@ng current (AC)
AC (alternating current): movement of electric charges periodically changes
direction
Mains power: 110 V
RMS
, 60 Hz
Actually, this is the rootmeansquare (RMS) voltage = V
0p
/sqrt(2)
5
Direct current (DC)
Current flowing in
one
direction
(typically static or changing slowly)
Exact nature of voltage depends
on power source
6
DC circuit
e.g. battery
Can think of this as movement of
electrons from source potential
–
to
+
around the circuit
However, convention in electronics, current
moves from + to – in the circuit. This can be
imagined as a movement of the charge as
l
holes
z
(i.e., absence of electrons), which
is especially useful for semiconductors
(diodes, transistors).
What will determine the amount of
current that will move through the
circuit for a given voltage?
7
Ohm
`
s Law
Convention
: current flows from + to – in the circuit
What is voltage here?
e.g. +3 V and 3V
What is voltage here?
Voltage drop
across
the resistor
What is the
current in the
circuit?
8
Resistors: facts
Made of a compound, film or
resistance wire (e.g. nickel/chrome)
Important consideration: what is the
maximum dissipative power (W) that a
resistor can tolerate?
P = IV = I*(IR) = I
2
R
Resistors will burn out if the dissipative
power is too great!
Symbols:
9
Resistor nota@on
4 bands: 5% accuracy
10
Kirchhoﬀ
`
s Laws
1.
At any node in an electrical circuit, the
sum
of the
currents
flowing into that node is equal to the sum of the currents flowing
out of that node. (= conservation of charge)
⇒
For a
parallel
circuit of N resistors, the total current
I
into the
junction equals the sum of currents (I
1
+ I
2
+ I
3
+ …. + I
N
= I
total
)
⇒
For a
series
circuit of N resistors, the sum of the voltage
drops (IR
1
+ IR
2
+ IR
3
+ …. + IR
N
= V
source
)
I
t
I
1
I
2
2.
The directed sum of the electrical potential differences around
a closed circuit is zero (= conservation of energy)
11
Resistors in series
1.5 V battery
Current is the
same
everywhere
in the circuit.
)
(
2
1
2
1
R
R
I
IR
IR
IR
V
total
in
By analogy for N resistors in
series:
)
(
...
1
2
1
∑
N
N
total
in
R
I
IR
IR
IR
IR
V
What can this principle
be useful for?
12
Resistors in parallel
Voltage drop across each resistor identical, but current is
depends on resistance R.
In this case, total current = sum of currents
2
1
I
I
I
in
2
1
V
V
V
in
2
2
1
1
R
V
R
V
R
V
total
in
Know that
∑
N
i
total
R
R
1
1
1
In general:
What will happen when
one resistor has a much
higher value than the other
one?
13
Digital mul@meter (DMM)
Can measure resistances, voltage and
current (AC and DC).
N. B. In Lab Unit 1, will become familiarized with
measuring DC voltages.
If measure voltage, what do we want internal
resistance of the multimeter to be?
……………………………………
If measure current, what do we want internal
resistance of the multimeter to be?
………………………………………..
Why would you
NEVER
connect multimeter in
currentreading mode to
measure between 0 and
+1.5 V?
14
Equivalent circuits
3
2
3
,
2
1
1
1
R
R
R
1
R
2
,
3
1
2
0
1
4
0
1
1
3
.
3
!
)
(
67
.
0
)
(
3
.
13
9
)
(
15
A
V
R
V
I
total
Ω
?
?
15
Voltage divider
In this case, would it be safe to
measure the
current
between
0.8 V
AB
and 0.6 V
AB
for
instance?
What consequences would this
have for the circuit?
What would happen to the circuit if
we measured the
voltage
between
0.8 V
AB
and 0.6 V
AB
?
16
Examples
What is the current in this circuit?
Assume all resistors are
equivalent (100
Ω
), what is the
total resistance of these circuits?
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