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Chapter 20: Electric Current
What is current?
Wire connecting two charged plates.
Q
Plates get
discharged
quickly.
+++++++++++++
E
-----------
Bulb lights temporarily
Recall: Charging a capacitor requires separating charges.
Q
Rate of flow of
charge is current.
I
q
t
charge flowed. C
 ampere( A)
time interval. s
Conventional current is opposite to flow of electrons.
To maintain current one needs to keep separating
charge. That’s what a battery does and it maintains V.
Think, Answer; Talk to your neighbors, Answer
Consider the following four situations.
i) An ion (charge +Q) moves to the right.
ii) A neutral hydrogen atom (proton, +e, and light
electron, -e) moves right.
iii) A beam of electrons in a TV shoots right
iv) In an ionic solution, massive positive ions flow right,
light negative electrons flow with equal speed to the
left.
In which of these is the net current ZERO?
A: All of the above B: ii only C: iv only
D: ii and iv only E: Some other combo/??
Ohm’s law: Resistance
A battery in action
A battery separates charges through chemical process
and maintains positive and negative terminal.
The potential difference (V) between the
terminals of an ideal battery is called emf    .
Wbattery = q V  q
Resistivity
Resistance, R, of a wire depends on three things:
1. area, A
2. length, L
In ideal wire electrons can roam freely. There is no change
in potential along the wire.
But in real wire there are hurdles. So the electrons loose
potential energy while moving along a wire.
Unit of R:
Current through
pot. difference.
V
V
I


a resistance,
resistance
R
A
Metal wires, Cu, Ag, etc. have negligible resistance.
+++++++++
--------
3. material, 
L
(larger area smaller resistance)
(longer the wire more resistance)
Tungsten has 3 times more than copper.
A Unit = ?
L
A
Resistivity is an electric property of material. It doesn’t
depend on area and length.
R
R
If resistivity is zero, the material is called superconductor.
Problem: What is the resistance of a 4 m long and 2 mm
diameter copper wire? Resistivity of Cu = 1.8 x 10-8 m.
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Magnetic Levitation and high-speed train
Water flow analogy of Current flow
I

R
V

What role do superconductors play in the levitation?
Single resistor Circuit
Vt


I
Vt
R
Vb
Vb
Ground pot = 0
Voltage drops linearly from
upper to lower part of the
resistor.
V  Vt  Vb
Vt
Same as battery
voltage.
Power and Energy in Circuits
The energy dissipation rate is
called power
U
q
 V  I V
t
t
For an EMF source:
For a resistor:
P  I V  I 2 R
V 2

R
Pump
Think, Answer; Talk to your neighbors, Answer
A battery with voltage ("emf") of 5V is attached to
resistor R. (We choose VA=0.)
What is the voltage at points B, C, and D?
Vb
Once the charge reaches
the low potential, battery
Connecting wire. Same
does work to increase its
voltage everywhere.
potential.
Ohm’s law relates current, voltage and resistance as,
V
I
For ideal battery, V    emf 
R
P
What are the
analogous
components?
P  I
What is the resistance of
100 W rated bulb at 120 V?
50 W?
A: VB = VD =0, VC = 5
B: VB = 5, VC < 5, VD> 0
C: VB = 5, VC < 5, VD= 0
D: VB = VC = 5, VD=0
E: None of these.
Alternating Current Source and Power
An electric generator produces
oscillating emf or current.
2
   BA sin t where,   2 f 
T
 t 
or,   t   m sin t
m
i t 
R
 t 
Oscillating
  t  m
 sin t
current: i  t  
R
R
or, i  t   I sin t
p  t   i  t    t   I  sin 2 t
i t 
I
T
t
t
V and I are in phase in R.
2
Average Power and RMS Values
i t 
i  t   I sin t
I
Current in a light bulb
t
reverses direction 120
times in a second.
p (t )  IV sin 2 t  I 2 R sin 2 t
always positive.
p t 
So the power reaches a
maximum 120 times a sec
P
but bulb glows steadily.
Makes more sense to use
t
average power :
I
1
1
V
P  I 2 R  IV  I rmsVrms where, I rms 
and, Vrms 
2
2
2
2
2
 I rms R
Think, Answer; Talk to your neighbors, Answer
We say household outlet is 120 V. In fact, the voltage of
this AC source varies; the 120 V is
A. The peak value of the voltage.
B. The rms value of the voltage.
C. The minimum value of the voltage.
D.The average value of the voltage.
Think, Answer; Talk to your neighbors, Answer
Power transmission lines uses very high voltage. The
reason behind using high voltage is because
A. it is faster to transmit using high voltage.
B. it is safer to transmit using high voltage.
C. energy loss is less to transmit using high voltage.
Problem: A hair dryer dissipates 1160 W when plugged
into 120 V outlet. (a) What is the amplitude of voltage
coming out of the outlet?
(b) What is the resistance of the hair dryer heating coil?
(c) What is the rms and peak current through the dryer?
(d) What is the maximum power the dryer dissipates?
Household electricity
Why three pronged plug?
Electric outlet are grounded
parallel Circuits.
120 V
rms
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Electric fence
Up to 5 mA
- No harm
10 to 20 mA
- May cause
paralysis
100 to 300 mA
- May cause
ventricular
fibrillation
Energy used in a Household: Kilowatt hours
Energy consumed by a device, E  Pt J or watt seconds
Commonly used unit is larger i.e., kilowatt hours = 1 unit.
Problem: One evening you used a 240 W laptop, a 1380 W
space heater, two 120 W light bulbs for five hours. How
much will it cost if your utility company charges 11 cents
per unit?
Ground Fault Interrupter Circuit
In kitchen and bathrooms where floor is
damp, current may pass through your body.
The built in sensing circuit compares currents in the hot wire
and neutral wire. If the current in those two wires differs by
as little as 5 mA, the GFI disconnects the circuit.
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