Transcript Ch 22&23 Current Electricity

Physics I
Direct Current Electricity
DC
Assignment
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P&P22:1,3,10,13-16,32,62-64
P&P23:4,7,11,16,55,57-59,64-67
Circuit Practice:
http://www.picra.net/csk/physics/CircuitPro
blems.html
1. Current Electricity – charges in
motion
• A. Circuit – a continuous loop through
which electricity can flow. It must contain
– 1. Energy source – battery, generator
– 2. Conductor – copper wire is common
– 3. Load – device(s) that converts electrical
energy to other useful forms of energy
B. Circuit Types
• 1. Parallel Circuit more than 1 path is
provided for current to
flow
• 2. Series Circuit
- one path for
current to flow
Schematic Symbols
Ohm’s Law
R=V
I
E = IR
R, Resistance in Ohms, W
V, Voltage in volts, v
I, current in amperes, a
or
V = IR
E, voltage in volts, for the overall circuit
V, potential drop across a section of a circuit
2. Cardinal rules for Resistors
• A. Voltage or Electromotive Force (across
battery) is equal in parallel
• Vbattery = V1 = V2 = V3 = ...
• B. Current is additive in parallel
• Itotal = I1 + I2 + I3 + ...
Kirchhoff’s 1st Law or Junction Rule - the
total current entering a junction must
be equal to the total current leaving the
junction.
C. Resistance in Parallel
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Equivalent Resistance
Cardinal Rule for Req
• This is the concept of equivalent resistance. The
equivalent resistance of a circuit is the amount
of resistance which a single resistor would need
in order to equal the overall effect of the
collection of resistors which are present in the
circuit. For parallel circuits, the mathematical
formula for computing the equivalent resistance
(Req) is
• 1 / Req = 1 / R1 + 1 / R2 + 1 / R3 + ...
Series Circuit – only 1 path is
provided for current
Voltage is additive in series
• Vbattery = V1 + V2 + V3 + ...
Kirchoff’s 2nd Law or the Loop Rule: The
algebraic sum of the potential
differences that occur around a
complete circuit is equal to zero.
E - (V1 + V2 + V3 + …) = 0
Current in series
• Ibattery = I1 = I2 = I3 = ...
Ibattery = I1 = I2 = I3 =
V / Req
Which leads us to
• Rt = R1 + R2 + R3 + ...
• since the current is the same
Cardinal Rules - Series
• E = Vt = V1 + V2 + V3
• I t = I1 = I2 = I3
• Rt = R1 + R2 + R3
1/Ct = 1/C1 + 1/C2 + 1/C3
Or: Ct =
1
1/C1 + 1/C2 + 1/C3
Cardinal rules - Parallel
E = Vt = V1 = V2 = V3 = …
Voltages are equal in parallel
It = I1 + I2 + I3 + …
Current is additive in parallel
1/Rt = 1/R1 + 1/R2 + 1/R3
Or: Rt =
1
1/R1 + 1/R2 + 1/R3
Or As more resistance is added, the resistance
goes DOWN!! And the current goes UP!
Circuit breaker opens
Joule’s Law
E = I2Rt
E, quantity of energy in joules
I, current in amps
R, resistance in ohms
t, time in sec
E proportional to I2
Power, rate of doing work
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P = IV
P = I2 R
Energy, E = Power x time, j/s x s = joule
P, Power: watt = joule/sec
I, Current: ampere = coulomb/sec
V, Voltage: volt = joule/coulomb
R, Resistance: ohm
E, Energy: joule
Sample Problem
• 22/1 The current through a light bulb
connected across the terminals of a 125 v
outlet is 0.50 a. at what rate does the bulb
convert electric energy to light?
• P = IV
• P = (0.50 a)(125 v)
• P = 63 w
Meters
• Voltmeter – measure difference in
potential between 2 points in a circuit
– ALWAYS connected in parallel with the part
of the circuit to be measured (acts as a load)
http://www.facstaff.bucknell.edu/mastascu/elessonshtml/Measurements/MeasVolt.ht
ml
Ammeter – measures current
• ALWAYS placed in series in a circuit
• Be sure current does not exceed range of
meter (use rheostat or “tap” or set meter at
highest range, if possible)
The ammeter is placed in SERIES with one
lead of a circuit. It must be placed around the
correct way so the needle moves up-scale.
http://www.talkingelectronics.com/
html/CctSymbolsE-BookWeb/CircuitSymbolsE-BookWeb.html
Galvanometer
• Used to measure weak electric currents
only
Rheostat - variable resistor
1. Controls amount of current flow
2. Controls voltage across a load
3. Protects expensive instruments
Rules for Meter Usage
A.
B.
C.
D.
E.
Handle gently
Connect voltmeter in parallel
Connect ammeter in series
Polarity labels tell how to connect meters
Red (+) and Black (-)
1. + should be wired directly or though other
components to the + terminal of the voltage
source
Meter Rules Continued
F. When taking readings of unknown
amounts, start at highest range or just
tap
G. Know meter scales BEFORE closing a
circuit so accurate readings can be taken
quickly
H. Using tapping rule when first closing a
circuit so accurate readings can be taken
quickly
Meter rules, cont.
I. Have circuit approved before closing the
circuit
J. Report trouble immediately
K. AC & DC meters are NOT
interchangeable (unless so designed)
L. Avoid overheating
1. Joule’s Law Q = I2 RT / J
2. Q a I2
Problem Applications
15. continued
• On the prior slide, simplification
shown in the diagrams gives way to
what is needed to be done
mathematically using the Cardinal
Rules:
• Series: V is +, I is =, R is +
• Parallel: V is =, I is +, R is 1/R +
More practice at…
• http://www.picra.net/csk/physics/CircuitPro
blems.html
Other methods of determining
resistance
• Nature of the Material
• R = rL/A
 r is resistivity of a
conductor in Wcm
• L is length of
conductor, cm
• A is cross sectional
area of conductor,
cm2
• Wheatstone Bridge
Problem sample
• What is the resistance of Copper wire 20.
m long, 0.81 mm diameter at 20.0oC?
(Resistivity, rCu at 20.0oC = 1.72x10-6 Wcm)
• R = r L = 1.72x10-6 Wcm) (2000cm)
•
A
p(8.1x10-2cm)2
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4
• R=
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A Wheatstone bridge is a measuring instrument invented by Samuel Hunter Christie
in 1833 and improved and popularized by Sir Charles Wheatstone in 1843. It is used
to measure an unknown electrical resistance by balancing two legs of a bridge
circuit, one leg of which includes the unknown component. Its operation is similar to
the original potentiometer except that in potentiometer circuits the meter used is a
sensitive galvanometer.
Wheatstone's bridge circuit diagram.
In the circuit at right, Rx is the unknown resistance to be measured; R1, R2 and R3
are resistors of known resistance and the resistance of R2 is adjustable. If the ratio of
the two resistances in the known leg (R2 / R1) is equal to the ratio of the two in the
unknown leg (Rx / R3), then the voltage between the two midpoints will be zero and
no current will flow between the midpoints. R2 is varied until this condition is
reached. The current direction indicates if R2 is too high or too low.
Detecting zero current can be done to extremely high accuracy (see Galvanometer).
Therefore, if R1, R2 and R3 are known to high precision, then Rx can be measured
to high precision. Very small changes in Rx disrupt the balance and are readily
detected.
If the bridge is balanced, which means that the current through the galvanometer Rg
is equal to zero, the equivalent resistance of the circuit between the source voltage
terminals is:
R1 + R2 in parallel with R3 + Rx
http://en.wikipedia.org/wiki/Wheatstone_bridge
•
members.shaw.ca/roma/res_cap.html
Sources
• http://www.glenbrook.k12.il.us/gbssci/phys
/Class/circuits/u9l4a.html
• http://www.ieee.org/portal/cms_docs_iport
als/iportals/education/preuniversity/tispt/pd
f/lessons/serpar.pdf