DC CIRCUITS
Releasing Electric Energy – Current
●
Allow separated
+
and
–
charges to come back
together by making an electric “
circuit
”
–
i.e. a path connecting the + and – charges
●
Electric current
(symbol:
I
)
–
The flow of
+
charge from one location to another
–
Units
: Amperes (
A
) = Coulombs / second (
C/s
)
●
Current occurs when there is a “
voltage drop
” (
ΔV
)
–
Difference
in voltage between one location and another
–
Often due to a battery, capacitor, or generator
–
KE of moving charges can be used → electronic devices
+
–
Resistance and Ohm's Law
●
Resistor
–
Device that converts current to another form of energy
●
Resistance
–
Defined by “Ohm's Law”
–
Units
: Measured in Ohms (
Ω
)
–
Depends on
shape
of object and
resistivity
of material (
ρ
)
R
=
Voltage
drop
Current
R
=
V
I
R
=
L
A
“
Ohm's Law”
Limits of Ohm's Law
●
Ohm's Law fits most materials well
–
Although
resistivity (
ρ
)
depends strongly on
temperature
●
Counterexamples: “Nonohmic” materials
–
Superconductors
→ R=0(
!
) below certain temperature
–
Semiconductors
→ R can be changed drastically
Batteries and EMF
●
Ideally, a battery has constant
Δ
V
through its life
–
But
real
batteries are not ideal:
–
They have an “internal resistance” (
r
– notice lower case)
●
In general:
–
Where
ε
is called “
electromotive force
”
–
ε
is the “ideal” voltage of the battery
●
The more current a battery puts out:
–
The more voltage is “eaten” by internal resistance
A
B
V
AB
=
−
Ir
Power in Electric Circuits
●
Electric power used by resistor:
–
Units
: Measured in Watts (
W
)
–
Given by any of 3 equivalent expressions:
●
Resistors convert energy into a variety of forms:
Power
=
Energy
used
time
1,000 – 10,000 W
1000 W (avg. for 24 hrs)
P
=
VI
P
=
I
2
R
P
=
V
2
R
1 – 500 W
If not converted to
other “useful”
forms, the power
must be dissipated
as
heat
energy
Health Risks of Electric Currents
●
Burns
–
Electric power is dissipated as heat, which burns tissue
●
Convulsions
–
Current can cause violent muscle contractions → injury
●
Heart issues
–
Current can disrupt the heart's natural electrical rhythm
–
Current as little as 0.1 Amps can be lethal in this way
Circuit Diagrams
●
Used to describe circuits abstractly
●
Symbols
:
Battery
Resistor
Capacitor
Switch
+
V (or
ε
)
R
C
S
Voltmeter
V
Ammeter
A
Ground (V=0)
Circuit “Rules”
1) Any two points connected
by wires only
have same
V
–
So:
V
A
= V
B
→
Δ
V
AB
= 0
2) At an intersection of wires:
current in = current out
–
“
Kirchoff's Current Rule” →
I
1
+ I
2
= I
3
3) Sum of
ΔV
's
around closed loop must be
zero
–
“
Kirchoff's Voltage Rule” →
ΔV
battery
– ΔV
resistor
= 0
+
A
B
I
1
I
2
I
3
Connecting Circuit Elements
●
Series
(one end connected to next element)
–
Current
must be same for each element
●
Parallel
(both ends connected to next element)
–
ΔV
must be the same for each element
–
If a circuit element is removed / off:
–
The rest of the circuit is unaffected
●
Other
(both series and parallel – or neither)
+
+
Equivalent Resistance & Capacitance
Resistors
Series:
Parallel:
Capacitors
Series:
Parallel:
I
total
=
I
1
=
I
2
R
1
R
2
V
total
=
V
1
V
2
R
eq
=
R
1
R
2
R
1
R
2
V
total
=
V
1
=
V
2
I
total
=
I
1
I
2
1
R
eq
=
1
R
1
1
R
2
C
1
C
2
Q
total
=
Q
1
=
Q
2
V
total
=
V
1
V
2
1
C
eq
=
1
C
1
1
C
2
V
total
=
V
1
=
V
2
Q
total
=
Q
1
Q
2
C
eq
=
C
1
C
2
C
1
C
2
RC Circuits
●
Stored energy in a capacitor
–
Is released using a resistor (“
discharging
” the capacitor)
–
Of course, the capacitor must be “
charged
” first
Charging a capacitor
Current flows until capacitor voltage
equals the battery's
ε
+
q
=
Q
final
1
−
e
−
t
RC
Discharging a capacitor
Current flows until capacitor has zero
charge (and zero voltage)
q
=
Q
0
e
−
t
RC
=
RC
“
time constant”
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