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Series Circuits
• The current is the same in each device.
• The equivalent resistance of the circuit is the sum
of the individual resistances.
Rtotal = R1 + R2
Parallel Circuits
• The voltage of each device is the full
voltage of the EMF source (the battery)
• The total current is divided between
each path:
1
1
1
= +
Rtotal R1 R2
Circuits Problem:Bulbs in Series vs Parallel
A circuit contains a 48-V battery and two 240Ω light bulbs.
In which circuit does each bulb burn brighter?
RULE: THE MORE POWER DISSIPATED IN A BULB, THE
BRIGHTER IT IS.
P = IV
Parallel Bulbs Burn Brighter!
Circuits Problem:Bulbs in Series vs Parallel
If a bulb burns out - what happens to the other bulb in
each circuit? Does it go out? Is it brighter? Dimmer? Or?
In the series circuit, the burned out bulb will short the circuit and
the other bulb will go out.
In the parallel circuit the other bulb will have the same brightness.
Circuits Problem:3 Bulbs in Parallel
If one more bulb is added to each circuit
(3 bulbs total), how does the brightness
of the bulbs change? Or not?
In the parallel circuit, the bulbs DO NOT DIM.
WHY?
In parallel, each of the three equal
bulbs gets the full voltage of the battery source.
Is this getting something for nothing?
NO! Parallel circuits drain the battery faster!
Circuits Problem:3 Bulbs in Series
If one more bulb is added to each circuit
(3 bulbs total), how does the brightness
of the bulbs change? Or not?
In the series circuit, the bulbs DIM. WHY?
V = V1 + V2 + V3
In series, each of the three equal bulbs gets one third of the Voltage
(V/3) that a single bulb would get.
V / 3)
(
V
1 V 2 Psinglebulb
P=
=
=
=
R
R
9 R
9
2
2
Note: P=VI but I is due to the equivalent Resistance: I = V/Rs =V/3R
So the Current through each is 1/3 the current through a single bulb and
P=VI=V/3 x I/3 = VI/9 = P/9. The bulbs burn 1/9 as bright!
Circuits Problem:3 Bulbs in Parallel
If one more bulb is added to each circuit
(3 bulbs total), how does the brightness
of the bulbs change? Or not?
In the parallel circuit, the bulbs DO NOT DIM.
WHY?
In parallel, each of the three equal
bulbs gets the full voltage of the battery source.
V2
P=
= Psinglebulb
R
Is this getting something for nothing?
NO! Parallel circuits drain the battery faster!
Kirchhoff’s Rules
• Junction Rule:
Σ Iin = Σ Iout
• Loop Rule:
∑ ΔV = 0
closed
loop
•First use junction rule and assign values to the current - guess the directions!
•Then use the loop rule CONSISTENTLY (Clockwise) on each loop.
•Any capacitor acts as an open branch in a circuit once under steady state conditions
Single Circuit: Multiple Batts
What is the direction of current?
When polarities of the batteries are opposed, one gets CHARGED.
Multiple Loop Circuit
Book
I1
I3
I2
I1
I3
Find Everything
V = 15.0V, R1 = 10.0Ω,
R2 = 20.0Ω,
R2 = 30.0Ω,
YOU DO IT.
For the circuit shown, find the equivalent resistance of the
circuit, the total current drawn by the battery, and the
current through and the potential difference across each
resistor. Place your results in a table for ease of reading.
What is the current in the
reistors?
RC Circuits: Charging
The capacitor continues to charge until it reaches its maximum
charge (Q = Cε). Once the capacitor is fully charged, the current
in the circuit is zero and the The potential difference across the
capacitor matches that supplied by the battery.
http://www.phy.ntnu.edu.tw/ntnujava/index.php?topic=31
RC Circuit: Charging
• The charge on the capacitor varies
with time
q(t) = Cε(1 – e-t/RC) = Q(1 – e-t/RC)
τ is the time constant
• τ = RC
• The current can be found
ε −t RC
I( t ) = e
R
• The time constant τ has units of time represents the time required
for the charge to increase from zero to 63.2% of its maximum
• The energy stored in the charged capacitor is ½ Qε = ½ Cε2
RC Circuit: Charging
q(t) = Q(1 – e-t/RC)
I( t ) =
ε −t RC
e
R
Discharging a Capacitor in an RC
Circuit
• When a charged capacitor is
placed in the circuit, it can be
discharged
– q = Qe-t/RC
• The charge decreases
exponentiallyAt t = τ = RC,
the charge decreases to 0.368
Qmax
– In other words, in one time
constant, the capacitor loses
63.2% of its initial charge
• The current is:
dq
Q −t RC
I (t ) =
=−
e
dt
RC
HO RC Problem
Ground-Fault Interrupters (GFI)
• Special power outlets
• Used in hazardous areas
• Designed to protect people from electrical
shock
• Senses currents (of about 5 mA or greater)
leaking to ground
• Shuts off the current when above this level
Electric Shock
What causes electric Shock in the human body,
Voltage or Current?
•Electric Shock occurs when current is
produced in the body, which is caused by an
impressed voltage.
•Voltage is the CAUSE
•Current does the DAMAGE
Electric Shock
Current (A)
0.001
0.005
0.010
0.015
0.070
Effect
Can be felt
Painful
Causes involuntary muscle spasms
Causes loss of muscle control
If through heart, serious!
If current lasts for 1 s - FATAL!
Dry Skin Body Resistance: 500,000 Ω
Wet Skin Body Resistance: 1000 Ω
Is AC Deadlier than DC?
•
Low frequency (50 - 60 Hz) AC
currents can be more dangerous than
similar levels of DC current since the
alternating fluctuations can cause the
heart to lose coordination, inducing
ventricular fibrillation, which then
rapidly leads to death.
• High voltage DC power can be more
dangerous than AC, however, since it
tends to cause muscles to lock in
position, stopping the victim from
releasing the energised conductor
once grasped.
Frequency Matters
Question
What current would you draw if
you were unfortunate to shortcircuit a 120 V line with dry
hands? Wet hands?
Use Ohm’s Law! V = IR!
Dry Skin Body Resistance: 500,000 Ω
Wet Skin Body Resistance: 1000 Ω
Question
What current would you draw if
you were unfortunate to shortcircuit a 120 V line with dry
hands? Wet hands?
Use Ohm’s Law! V = IR!
DRY: I = V/R = 120 V/500,000 Ω = .00024 (live!)
WET: I = V/R = 120 V/1000 Ω = .12 (dead!)
Electric Shock Therapy
ELECTRO CONVULSIVE
THERAPY
An electric shock is applied to produce a convulsive seizure.
The shock is typically between 140 - 170 volts and lasts
between 0.5 and 1 seconds. No explanation of how it works.
Used in the treatment of:
1.Chronic endogenous depression
2.Bipolar disorder.
3.Acute mania.
4.Certain types of schizophrenia
In the U.S. 33,000 - 50,000 people receive ECT each year
HW Problem #2
HW2. The switch in the figure has been in position a for a long
time. It is changed to position b at t = 0s. What are the charge on the
capacitor and the current I through the resistor
a)immediately after the switch is closed?
b)What is the time constant τ ?
c)at t = 50 μs?
d)at t = 200 μs?