DC Circuits (notes)

piquantdistractedElectronics - Devices

Oct 5, 2013 (3 years and 9 months ago)

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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

Counter-examples: “Non-ohmic” 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”