Electric Current and Direct Current Circuits

1
Electric Current andDirect Current Circuits

• Physics 112, Prof. C.E. Hyde-Wright
• Spring 2003
• Walker, Chapter 21

2
Electric Current
Whenever there is a net movement of charge, there
exists an electrical current. A current can
flow in a wire usually electrons. A current can
flow in a liquid solution For example Na, and
K ions across a nerve cell membrane. A current
can flow in air or free space electron or ion
beam, lightning.
3
Unit of measure of Electric Current

• If a charge ?Q moves through a surface A in a
  time ? t, then there is a current I
• The unit of current is the Ampere (A) 1 A 1
  Coulomb/sec.
• By convention, the direction of the current is
  the direction of flow of the positive charges.
• If electrons flow to the left, that is a
  positive current to the right.

e-
I
4
Current and Resistance
In most materials, in order for a current I to
flow there must be a potential difference, or
voltage V, across the conducting material. A
voltage difference means there is an electric
field providing a force to push the charges. The
free charges travel at a constant (average)
velocity and do not accelerate because the free
charges bounce off the fixed charges in the
medium. This provides a friction, or braking
force that balances the external electric force.
V1
V2
V1 gt V2
e-
E
5
Ohms Law

• For many materials, the current I is directly
  proportional to the voltage difference V.
• We define the resistance, R, of such a material
  to be
• The unit of resistance is Ohms (W) 1 W 1
  Volt/Amp
• Common resistors used in electrical circuits
  range from a few W to MW (106W).
• If R is constant doesnt depend on current, or
  history of current flow, and only small variation
  with temperature, atmospheric pressure, etc,
• the material is said to be ohmic, and we write
  Ohms Law

6
Fluid Analogy of Resistance

• A fluid (liquid or gas) will not flow through a
  narrow tube unless there is a pressure difference
  between the input and output ends.
• The pressure difference can be provided by
  external pressure, or by gravity.
• The longer the tube, or the narrower the tube,
  the larger a pressure difference (or gravity
  gradient) is required to maintain the same flow.

Fluid flow
Liquid flow
7
Resistivity
An object which provides resistance to current
flow is called a resistor. The actual
resistance depends on properties of the
material (resistivity) the geometry (length
and cross sectional area) For a conductor of
length L and cross-sectional area A, the
resistance is R?L/A, where ? is called the
resistivity.
L
r
Area A
8
Wires Resistors in Circuits

• A piece of wire is a resistor.
• However, for good conductors like Cu, Al, Au, Ag,
  the resistivity is extremely low.
• When we analyze a circuit containing wires and
  other elements (such as light bulbs), the
  resistance of the wires is so low that we can
  pretend the wires are perfect conductors.
• Current can flow in the wire even though the
  potential is everywhere the same inside each
  separate piece of wire.

9
Temperature Dependence and Superconductivity
The resistivity of most materials depends on the
temperature. For most metals, resistivity
increases linearly with temperature over a
range This temperature dependence to
resistivity can be exploited to build a
thermometer Measure the Voltage required to
maintain a fixed current in the resistor. Changes
in V measure changes in the temperature of the
medium surrounding the resistor. Some materials
(Pb, Nb, Nb3Sn, YBa2Cu3O7) when very cold (3 to
20 K), have a resistivity which abruptly drops to
zero. Such materials are then superconductors.
10
Sample Resistivity values
11
Resistors in Circuits

• In drawing a circuit, the symbol for a resistor
  is
• This zigzag pattern is a visual reminder that the
  material of the resistor impedes the flow of
  charge, and it requires a potential difference V
  between the two ends to drive current through the
  resistor.
• Current flows from higher value of potential to
  lower value of potential

12
Simple Battery Circuit

• A battery is like a pump
• A pump raises fluid by a height h.
• A battery pumps charge up to a higher potential.

I V/R
Current is the same everywhere. Voltage varies
from point to point around loop.
13
Power in Electric Circuits
Recall that resistance is like an internal
friction - energy is dissipated. The amount
of energy dissipated when a charge DQ flows down
a voltage drop V in a time Dt is the power P P
?U/? t (DQ/Dt)V IV SI unit watt, W AmpVolt
C V/s J/s For a resistor, PIV can be
rewritten with Ohms Law VIR, P I2R
V2/R Power is not Energy, Power is rate of
consumption (or production) of energy Large power
plants produce between 100 MW and 1GW of power.
14
Energy and Power

• Energy Usage Power times time Energy consumed
• 1 kilowatt-hour (1000 W)(3600 s) (1000
  J/s)(3600 s) 3.6?106 J
• Electricity in VA costs about 0.10 per KW?hr
• My household uses of 1KW of power, on average.
• There are 8800 hours in a year
• In one year, we consume 8800 KW?hr, or 3.2 ?
  1010 J

15
Direct Current (DC) Circuits A circuit is a loop
comprised of elements like resistors and
capacitors around which current flows. For
current to continue flowing in a circuit with
non-zero resistance, there must be an energy
source. This source is often a battery. A
battery provides a voltage difference across its
terminals.
Batteries and Electromotive Force (emf) Any
device which increases the potential energy of
charges which flow through it is called a
source of emf. The emf is measured in volts and
often written as e. The emf may originate from a
chemical reaction as in a battery or from
mechanical motion such as in a generator.
16
Direct Current (DC) Circuits - MORE
Includes batteries, resistors, capacitors
Kirchoffs Rules - conservation of charges
(Laws) follow from (junction rule, valid at
any junction) - conservation of
energy (loop rule, valid for any loop)
With emf (?) constant current can be
maintained charge pump forces electrons to
move in a direction opposite to the electric
field SI unit for emf Volt (V) No
resistance connecting wires of the loop
17
A simple circuit with a battery and resistor can
be graphically represented as r is
known as the internal resistance of the battery.
The voltage on the terminals of the battery is,
therefore, V ? - Ir and the current in the
circuit is
18
Battery as emf in the DC Circuits

terminal at higher potential then -
terminal V?-Ir V terminal voltage r
internal resistance ? - equivalent to
open-circuit (I0) voltage
I
Charge potential increases by ? Charge potential
decreases by Ir
-
I
r
Terminal voltage
Emf
?I
Total power of emf
Power dissipated as joule heat in
Internal resistor
Load resistor
19
Combining Circuit Elements Any two circuit
elements can be combined in two different
ways in series - with one right after the
other, or in parallel - with one right next to
the other. Series Parallel Combination
Combination
20
Equivalent Resistance The current I is the
same in both The current may be different in
resistors, so the voltage Vba must each
resistor, but the voltage satisfy
Vba is the same across each VbaIR1IR2I(R1R2)
resistor and the total current is
conserved II1I2 ReqR1R2 1/Req 1/R11/R2
21
Kirchhoffs Rules Any charge must move around
any closed loop with emf Any charge must gain
as much energy as it loses Loss IR
potential drop across resistor Gain chemical
energy from the battery (charge go reverse
direction from ?) Often what seems to be a
complicated circuit can be reduced to a
simple one, but not always. For more complicated
circuits we must apply Kirchhoffs Rules
Junction Rule The sum of currents entering a
junction equals the sum of currents leaving
a junction. Loop Rule The sum of the potential
difference across all the elements around
any closed circuit loop must be zero.
22
Circuits containing Capacitors
Capacitors are used in electronic circuits. The
symbol for a capacitor is We can also combine
separate capacitors into one effective or
equivalent capacitor. 2 capacitors can be
combined either in parallel or in series.
Series Parallel
Combination Combination
C2 C2
C1 C2
23
Parallel vs. Series Combination Parallel Se
ries charge Q1 , Q2 charge on each
is Q total QQ1 Q2 total charge is
Q voltage on each is V voltage V1 , V2
Q1C1V QC1V1 Q2C2V QC2V2
QCeffV QCeff(V1V2) CeffC1C2
1/Ceff1/C11/C2
24
RC Circuits We can construct circuits with more
than just resistor, for example, a resistor, a
capacitor, and a switch When the switch is
closed the current will not remain constant.
Capacitor acts as an open circuit I0 in
branch with capacitor under study state
condition.
25
Capacitor Charging Lets assume that at time t0,
the capacitor is uncharged, and we close the
switch. We can show that the charge on the
capacitor at some later time t
is qqmax(1-e-t/RC) RC is known as the time
constant ?, and qmax is the maximum amount
of charge that the capacitor will
acquire qmaxCe
26
Capacitor Discharging Consider this circuit with
the capacitor fully charged at time t0 It
can be shown that the charge
on the capacitor is
given by qqmaxe-t/RC
27
Ammeters and Voltmeters
28
(No Transcript)