Ammeter & Voltmeter
Ammeter, A, inserted into the circuit.
I
Voltmeter, V, across the
circuit element.
I
2/21/2016
1
Galvanometer
=
Rg
Ig
I g ~ 50  100  A for full scale deflection.
Rg ~ 100 
2/21/2016
2
Make a 1.0 Ampere full scale deflection
ammeter
Vg  Rg I g  I P RP
RP  Rg
Ig
IP
 Rg
Ig
I  Ig
small parallel
resistor (shunt)
If Rg = 100  and Ig = 50 A, then
6
6
50  10 A
50  10 A
RP  100 
 100 
 0.005 
6
1 A  50  10 A
1A
To change the scale, change RP .
2/21/2016
3
Voltmeter
Assume Rg = 100  and Ig = 50 A for full scale
deflection (typical). Make a 100 V full scale deflection
voltmeter.
I g ( RS  Rg )  V
100 V
6
RS  Rg 

2

10

6
50  10 A
100  negligible
2/21/2016
4
Ohmmeter
2/21/2016
5
RC Circuits
2/21/2016
6
RC Circuits
• Charging a capacitor:
C initially uncharged; connect
switch to a at t=0
Calculate current and charge
as function of time.
q
• Apply Kirchhoff’s Voltage Law:    IR  0
C
• Short term: q  q0  0
  0  I0 R  0

I0 
R
• Long term: I  I   0
q
   0R  0
2/21/2016
C
Intermediate term:
q dq
  R0
C dt
q  C
7
Solution
dq 
q
 
dt R RC
q
dq
0  / R  q / RC  0 dt
X   / R  q / RC

 RC
q
R RC


t
t
dX
  dt
X
0
1
dX 
dq
RC

q
R RC
ln x 

R
R
e
2/21/2016
t

RC
q 

 R  RC  t
 ln 




 RC
 R 
q
1
C
8
Continued
Capacitive Time Constant: 
The greater the , the
greater the charging time.
  RC
q  C (1  e
 t /
)
dq   t /
I
 e
dt R
Units of  :
ΩF 
q
Vc    (1  e  t / )
C
2/21/2016
VC
C

s
A V C/s
9
Charging a Capacitor
q  C (1  e
at
 t /
)
t0
t
t 
I

R
e
t /
at t  0
t
t 
2/21/2016
10
Charging a Capacitor
2/21/2016
11
RC Circuits
• Discharging a capacitor:
• C initially charged with Q=C
• Connect switch S2 at t=0.
q
 IR  0
• Apply Kirchhoff’s Voltage Law:
C
• Short term: q  q0  C
  I0 R  0
I0 

R
• Long term: I  I   0
Intermediate term:
q dq

R0
C dt
q  0  R  0
2/21/2016
q  0
12
Solution
q
dq q
R
 0
dt C
t
dq
dt
C q  0  RC
t
q
q

 ln q C  ln
RC
C
q  C e

t
RC
dq 
I 
 e
dt R
2/21/2016

t
RC
13
Discharging a Capacitor
q  C e

t
RC

t
RC
t0
t
at
t 
I
at

R
e
t0
t
t 
2/21/2016
14
Behavior of Capacitors
• Charging
– Initially, the capacitor behaves like a wire.
– After a long time, the capacitor behaves like an open
switch in terms of current flow.
• Discharging
– Initially, the capacitor behaves like a variable battery.
– After a long time, the capacitor behaves like an open
switch
2/21/2016
15
Magnetic Field
• Large Magnetic fields are used
in MRI (Nobel prize for
medicine in 2003)
• Extremely Large magnetic field
are found in some stars
• Earth has a Magnetic Field
2/21/2016
22
Bar Magnets
• Bar magnet ... two poles: N and S
Like poles repel; Unlike poles
attract.
• Magnetic Field lines: (defined in
same way as electric field lines,
direction and density)
N
S
S
N
N
N
S
S
Attraction
S
2/21/2016
N
Repulsion
From North to South
23
DEMO of Magnetic Field Lines
Electric Field Lines
of an Electric Dipole
Magnetic Field Lines
of a bar magnet
2/21/2016
S
N
24
Magnetic Monopoles
• One explanation: there exists magnetic charge, just like
electric charge. An entity which carried this magnetic
charge would be called a magnetic monopole (having +
or - magnetic charge).
• How can you isolate this magnetic charge?
Try cutting a bar magnet in half:
S
N
S
N
S
N
• In fact no attempt yet has been successful in finding
magnetic monopoles in nature but scientists are
looking for them.
2/21/2016
26
Earth’s Magnetic Field
By convention, the N end of
a bar magnet is what points
at the Earth’s North
Geographic Pole.
Since opposite poles attract
(analogous to opposite
electric charges), the “North
Geomagnetic Pole” is in
fact a magnetic SOUTH
pole, by convention.
Confusing, but it’s just a
convention. Just remember
that we define N for bar
magnets as pointing to
geographic North.
2/21/2016
27
Earth’s Magnetic Field
Magnetic
North Pole
1999
2/21/2016
28
Earth’s Magnetic Field
Magnetically
Quiet
Day
Magnetically
Disturbed
Day
2/21/2016
29
Earth’s Magnetic Field
Since 1904:
750 km,
an average of 9.4 km per year.
From 1973 to late 1983:
120 km,
an average of 11.6 km per year
2/21/2016
30
Earth’s Magnetic Field