Transcript Electric Current

Current
• Electric Current (I)
– The rate at which charge flows through a
perpendicular surface
dQ
I
dt
C/s or Ampere, A
The current has the same direction as the flow of positive
charge.
Current
• Direct Current (DC)
– The constant current in magnitude and
direction
• Alternating Current (AC)
– The current changing in magnitude and
direction all the time
Current
Q  (nAvd t )q
Q (nAvd t )q
I av 

 nqvd A
t
t
vd : drift speed of charge q
n : number of mobile charge carriers per unit volume
Quiz #1
• Consider positive and negative charges
moving horizontally through the four regions
shown in the figure. Rank the current in
these four regions, from lowest to highest.
current density
• The current density (J)
– the current per unit area
I
J   nqvd
A
J  nqvd
current density
• A current density J and an electric field E are
established in a conductor whenever a potential
difference is maintained across the conductor
J E
Ohm’s law
: conductivity
Resistance
J
V  Vb  Va  El  

= 1/ : Resistivity
  I
l  
  A

 l 
 l  I     IR

 A
l
Resistance (.m)
R
A
Resistivity
Resistors
Resistance
Resistance and Temperature
Conductor
  0 1   (T  T0 )
R  R0 1   (T  T0 )


 0 T
temperature coefficient of resistivity
Resistance and Temperature
Semiconductor
superconductor
• a class of metals and
compounds whose
resistance decreases to
zero when they are below
a certain temperature Tc,
known as the critical
temperature
superconductor
• A small permanent
magnet levitated
above a disk of the
superconductor
Ba2Cu3O7, which is
at 77 K.
Electrical Power (P)
• The rate at which energy is delivered to
a resistor
(V )2
P  I V 
 I 2R
R
Example #7
• For the two lightbulbs
shown in figure, rank
the current values at
points a through f,
from greatest to least
Direct Current Circuits
• Electromotive Force
• Resistors in Series and Parallel
• Kirchhoff’s Rules
• RC Circuits
• Electrical Meters
Electromotive Force
• Describing not a force but rather a
potential difference in volts
• A battery is called either a source of
electromotive force, or more
commonly, a source of emf
Electromotive Force
• The emf of a battery
is the maximum
possible voltage that
the battery can
provide between its
terminals
Circuit Diagram
V  Va  Vb    Ir
r = internal resistance
IR    Ir
I

Rr
R = load resistance
Power  I   I R  I r
2
2
Example #8
• A battery has an emf of 12.0 V and
an internal resistance of 0.05 . Its
terminals are connected to a load
resistance of 3.00 .
Resistors in Series
V  IR1  IR2  I ( R1  R2 )  IReq
Req  R1  R2
Resistors in Parallel
 V
I  I1  I 2  
 R1
  V

  R2
  V
  
  Req



1
1 1
 
Req R1 R2
Example #9
• Four resistors are
connected as shown
in the figure,
– Find the equivalent
resistance between
points a and c
– What is the current in
each resistor if a
potential difference
of 42 V is maintained
between a and c
Example #10
• Three resistors are connected in
parallel as shown in the figure
28.11 . A potential difference
of 18.0 V is maintained
between points a and b
– Find the current in each resistor
– Calculate the power delivered to
each resistor and the total power
delivered to the combination of
resistors
– Calculate the equivalent resistance
of the circuit
Kirchhoff’s Rules
• Junction rule.
– The sum of the currents entering any junction
in a circuit must equal the sum of the currents
leaving that junction
I
in
  I out
Kirchhoff’s Rules
• Loop rule.
– The sum of the potential
differences across all
elements around any
closed circuit loop must be
zero

CosedLoop
V  0
Example #11
• A single-loop circuit contains two
resistors and two batteries, as
shown in the figure (Neglect the
internal resistances of the
batteries.
– Find the current in the circuit.
– What power is delivered to each
resistor?
– What power is delivered by the 12-V
battery?
Solution #11
The 12-V battery delivers power
Example #12
• Find the currents I1, I2,
and I3 in the circuit
shown in the figure.
Solution #12
RC Circuits
• Charging a Capacitor
q
   IR  0
C
RC Circuits
• Charging a Capacitor

I0 
R
current at t = 0
Q  C
maximum charge
t



RC
q(t )  Q 1  e 


  RC
time constant of the circuit
I  I 0e

t
RC
RC Circuits
• Discharging a Capacitor
q
  IR  0
C
q(t  0)  Q
Charge at t = 0
q(t )  Qe

t
RC
t

dq(t )
Q  RCt
I (t ) 

e
  I 0e RC
dt
RC
Electrical Meters
• The Galvanometer
– the main component in
analog meters for
measuring current and
voltage
Electrical Meters
• The Ammeter
– A device that
measures
current
Electrical Meters
• The Voltmeter
– A device that
measures
potential
difference
Quiz #2
• Find the equivalent
resistance between
points a and b in the
figure
• If a potential difference
of 34.0 V is applied
between points a and b.
calculate the current in
each resistor.