DC circuits, Kirchhoff s Laws •  Alternating Current (AC), Direct Current (DC)
•  DC Circuits
•  Resistors
•  Kirchhoff s Laws
CHM6158C -­‐ Lecture 2 1 Electric current Movement of electrons in a conductor
Examples of good conductors:
•  copper
•  aluminum
Cable enclosed with an insulating
•  silver
material (e.g. polyethylene)
At what speed does
electricity propagate?
Units:
http://www.hydroquebec.com/learning/images/questceque/i_schema_atome.gif
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
A current of 100 mA can be lethal !
2 Conduc@vity Conductivity = measure of a material s ability to conduct an electrical current
silver > copper > aluminum
Inverse: Resis@vity vs. Resistance Resistivity = measure of how strongly a material opposes the flow of electrical
current (units: Ω m) (inherent of material)
Strange units –
why?
E
ρ=
J
Magnitude of electric field (V / m)
Magnitude of current density (A / m2)
Resistance = measure of how strongly a material opposes the flow of electrical
current (units: Ω ) (dependent on cross-section and length of material)
OHM s LAW
V
R=
I
3 Alterna@ng current (AC) AC (alternating current): movement of electric charges periodically changes
direction
Mains power: 110 VRMS, 60 Hz
Actually, this is the root-mean-square (RMS) voltage = V0-p/sqrt(2)
4 Direct current (DC) Current flowing in one direction
(typically static or changing slowly)
Exact nature of voltage depends
on power source
5 DC circuit Can think of this as movement of
electrons from source potential – to +
around the circuit
e.g. battery
However, convention in electronics, current
moves from + to – in the circuit. This can be
imagined as a movement of the charge as
holes (i.e., absence of electrons), which
is especially useful for semi-conductors
(diodes, transistors).
What will determine the amount of
current that will move through the
circuit for a given voltage?
6 Ohm s Law Convention: current flows from + to – in the circuit
What is voltage here?
Voltage drop across
the resistor
e.g. +3 V and -3V
What is voltage here?
What is the
current in the
circuit?
7 Resistors: facts Made of a compound, film or
resistance wire (e.g. nickel/chrome)
Symbols:
Important consideration: what is the
maximum dissipative power (W) that a
resistor can tolerate?
P = IV = I*(IR) = I2R
Resistors will burn out if the dissipative
power is too great!
8 Resistor nota@on 4 bands: 5% accuracy
9 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)
It
I1
I2
⇒ For a parallel circuit of N resistors, the total current I into the
junction equals the sum of currents (I1 + I2 + I3 + …. + IN = Itotal)
2. The directed sum of the electrical potential differences around
a closed circuit is zero (= conservation of energy)
⇒ For a series circuit of N resistors, the sum of the voltage
drops (IR1 + IR2 + IR3 + …. + IRN = Vsource)
10 Resistors in series Current is the same everywhere
in the circuit.
What can this principle
be useful for?
1.5 V battery
Vin = IRtotal = IR1 + IR2 = I ( R1 + R2 )
By analogy for N resistors in
series:
N
Vin = IRtotal = IR1 + IR2 + ...IRN = I (∑ R)
1
11 Resistors in parallel What will happen when
one resistor has a much
higher value than the other
one?
Voltage drop across each resistor identical, but current is
depends on resistance R.
In this case, total current = sum of currents
Know that
Vin = V1 = V2
In general:
N
1
1
=∑
Rtotal
1 Ri
I in = I1 + I 2
Vin
V1 V2
= +
Rtotal R1 R2
12 Digital mul@meter (DMM) Can measure resistances, voltage and
current (AC and DC).
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
current-reading mode to
measure between 0 and
+1.5 V?
N. B. In Lab Unit 1, will become familiarized with
measuring DC voltages.
13 Equivalent circuits 1
1
1
=
+
R2,3 R2 R3
? 1
1
1
1
=
+
=
R2,3 20 40 13.3!
V
15(V )
I=
=
= 0.67 ( A)
? Rtotal 9 + 13.3(Ω)
14 Voltage divider In this case, would it be safe to
measure the current between
0.8 VAB and 0.6 VAB for
instance?
What consequences would this
have for the circuit?
What would happen to the circuit if
we measured the voltage between
0.8 VAB and 0.6 VAB?
15 Examples What is the current in this circuit?
Assume all resistors are
equivalent (100 Ω), what is the
total resistance of these circuits?
16