Download Conductors and insulators

Why does a light bulb burn out when you switch the
light on and never when you turn it off?
The amount of current
i
drawn by a given device is determined by its power input
P
P  Vi  i 
V
The current in a 100-W light bulb is
P 100 W
i 
 0.83 A
V 120 V
V 120 V
R 
 144
i 0.83 A
A kitchen circuit
An 1800-W toaster, a 1.3-kW electric
frying pan, and a 100-W lamp are
plugged into the same 20-A, 120-V
circuit.
a) What current is drawn by each device,
and what is the resistance of each
device?
b) Will this combination blow the fuse?
To prevent the fuse from blowing, you replace the fuse with one rated at 40 A.
Is this a reasonable thing to do?
Pi R
2
Wheatstone bridge
Charles Wheatstone
British scientist and
inventor
1802-1875
Samuel Hunter Christie, British scientist and mathematician
Wheatstone English concertina
Electromotive force
Second exam Tuesday, March 22, 7 pm
105-107 Heldenfels
Sections 521, 522 room 105
Sections 523, 525 room 107
Section 526 room 109
Gauss’s Law
The total flux of electric field out of any
closed surface is equal to the charge
contained inside the surface divided by  0 .
  Qenclosed
 E  dS 
S
0
Conductors and insulators
Charges reside at the surface of the conductor
+
+
+ +
+
+
+
+
+
Conductor
E=0
+
+
+
+
+
+
Electric field of a ball of charge
Q
1
Q
rR E
40 r 2
1
rQ
rR E
40 R 3
Electric field outside of a charged sphere is exactly the
same as the electric field produced by a point charge,
located at the center of the sphere, with charge equal to the
total charge on the sphere.
Insulating sphere with charge Q uniformly spread throughout the volume
A
E
1
Q
rA E
40 r 2
A
rA E
r
Q
40 A
3
r
Conducting sphere with charge Q
A
E
r A E0
rA E
V
A
r
1
Q
40 r 2
1 Q
rA V 
40 A
1
Q
40 A
r
rA V 
1 Q
40 r
A Charged, Thin Sheet of Insulating Material
+
+
+
+
+
+
+
+
+
+
+

E
2 0
Electric field near a surface of a conductor
l
a
 
 E  dS 
 EdS  Ea
cap
a
Ea 
0

E
0

 A
QL
 [V (top)  V (bottom)]   L  
L
0
0 A
0 A
QL
V 
A 0
The capacitance is:
A 0
Q
Q
C


QL
V
L
A 0
Spherical capacitor; Cylindrical capacitor
Current Density
 
i   j  dS
S
Consider current flowing in a homogeneous wire with cross sectional
area A.
 
i   j  dS   jdS  j  dS  jA
A
A
i
j
A
A
for j =Const only!
Current, Ohm’s Law, Etc.
dQ
i
dt
V
Ohm ' s Law : R  ; R  Const (independent of V )
i
l
R
A


j  E


E  j
For steady state situation
 
j

d
S

0

 
 E dr  0
1.Kirchhoff’s junction rule: The algebraic sum
of the currents into any junction is zero.
2.Kirchhoff’s loop rule: The algebraic sum of
the potential differences in any loop must be
zero.
Joule’s Law
2
V
P  Vi  i R 
R
2