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Transcript
Do Now: An appliance uses 450 kJ of
energy over 1 hour when connected with a
p.d. of 120-V. What is the resistance of the
appliance?
•
•
•
•
W = V2t/R
R = V2t/E
R = (120V)2(3600 s) / 450x103 J
115 W.
Sketching with Circuit Symbols
To represent components on
circuit use symbols.
See ref tables
Circuit
Symbols
1. Use your tables to sketch the
circuit below with the appropriate
symbols
2 Types of Circuits
• Series – single pathway
for current flow.
Components connected
in succession like a chain.
• Parallel – pathway with
more than 1 branch –
wire splits.
Analyzing Components on
Electric Circuits
Each component on a circuit has its own
current, voltage, resistance.
How can those variables be determined
for individual resistors in circuits?
Use Ohm’s Law for individual components:
I1 = V1/R1
V1 = I1R1 or R1 = V1/I1
Or to analyze total current, voltage
resistance for the entire circuit.
Itot = Vtot/Req
Vtot = ItotReq
Req = Vtot/Itot
The power supply (battery) provides the
total E, the components may share
(divide) the total E (p.d.), current, or
both.
Analyzing Series Circuits
Series circuits are a chain of components
connected in a circle. Charges have 1 path.
Because of the conservation of
charge, & because there is only one
route, the current (I) is the same
through every component.
I1 = I2 = I3 = I4 …
2. the reading on ammeter 1 is 3-A,
what is the reading on ammeter 4?
1.
4.
2.
3.
Resistance
As more resistors are added in a series
connection, the total equivalent resistance of
the circuit increases.
equivalent resistance is the simple addition
of each resistor on the circuit.
R1 + R2+ R3 = Req.
3. Given the circuit:
2-W.
4-W.
6-W.
What is the equivalent resistance?
Voltage on a series circuit.
The battery, or generator or source
provides the Vtot for the circuit.
The Vtot is the addition of each p.d. across
each resistor on the circuit.
V1 + V2+ V3 ~ Vtot.= the battery voltage
4. Given the circuit:
1-V.
2-V.
3-V.
What is the total circuit voltage?
What is the battery voltage?
6V
5. The p.d. or V across each resistor can be found:
V1 = IR1.
V2 = IR2.
V3 = IR3.
• If resistance on V3 is 3 W, and the current is 1 A, what
is the voltage V3?
V = IR = (3W)(1A) = 3V
• What is the current through bulb 1?
1A
• What will happen if one of the bulbs burns out?
Since there is only one path for
the charges to follow, if one
conductor (resistor) is
disconnected, the circuit is
broken. The current flow stops.
The bulbs go out.
Since the devices must share
the voltage, as more are added
the energy of the charges
decreases. The bulbs become
dimmer.
In Class tx pg 745 #4a, 4c.
• Read txt 730 – 739 do 739 #1, 2, 4, 5
• For problem 1,2 above sketch the circuit
along side of the calculations w proper
symbols for problem solving.
Parallel Circuits
What’s Different?
The current reaches a fork, can choose
path.
Through which resistor does more charge flow?
Why?
Sketching: Make rungs or branches.
• Resistors all connected across the V , all V equal to
the battery voltage.
• V1 = V2 =V3 = Vtot
• Current (I), charges reach a junction, they divide.
• Itot in the circuit = S currents in each branch.
• Itot = I1 + I2 + I3 …
• Individual currents
• I1 =V
R1
Resistance goes down as more branches are
added:
1/Req = 1/R1 + 1/R2 + 1/R3 …
Where Req is the equivalent or total resistance.
*Because resistance is a
reciprocal relationship, the Req
must be less than the smallest
resistance on the circuit. As
you add resistors, the
resistance goes down!!
Since parallel circuits offer
more than one path for the
charge to flow, individual parts
can be disconnected and
charge will still flow through
other branches.
Since the voltage is equal on
each branch, adding more
branches does not reduce the
energy each branch receives.
Add more bulbs, the others
stay bright!
Ex 1: A 9V battery is connected in series to 2 bulbs: 4W,
& 2W.
A) Sketch the diagram with the proper symbols. Show
real and conventional current flow direction.
B) Find the equivalent or total resistance on the
circuit.
C) Find the total current in the circuit.
D) What is the voltage in each branch?
E) Find the current in each branch.
Ex 2: A 9V battery is connected in parallel to 2
bulbs: 4W, & 2W.
A) Sketch the diagram with the proper symbols.
Show real and conventional current flow
direction.
B) Find the equivalent or total resistance on
the circuit.
C) Find the total current in the circuit.
D) What is the voltage in each branch?
E) Find the current in each branch.
F) Add the currents from each branch together.
How do they relate to the total current?
G) Now add a 3 W bulb to the circuit.
Recalculate the equivalent resistance.
H) How does the new resistance on the
circuit compare to the original?
I) Recalculate the power of each bulb.
J) What happened to the bulbs’ brightness when
the 3W bulb was added?
Summery
Parallel. Add resistance, total
• Itot goes up.
• Req goes down.
• Indiv. P/ Brightness
equal.
• Lowest R = most P
brightest.
• Remove 1, others stay on
same power/brightness
Series. Add resistance, total
• Itot goes down
• Req goes up.
• Indiv P/brightness
decrease.
• Highest R = bright/most P
• Remove 1, others go out.
• Less bulbs each is
brighter.
Hwk:Text pg 745 #2 - 5.
Sketch the circuits in #4, 5.
Power = Brightness
The bulb brightness in each resistor is
dependent on the power in each resistor.
P = VI
P = I2R P = V2/R,
can calculate the power and deduce the
brightness.
Which equation is more useful for:
• Series?
P = I2R
• Parallel?
P = V2
R
Ex 2: 2 bulbs in series connected to 6V cell.
R1 = 2W, R2 = 4 W.
Find the power in each.
What is relative brightness?
What if the 2W is removed? What happens
to the brightness of the remaining bulbs?
Ex 3: 3 bulbs in parallel connected to 6V cell. R1
= 2W, R2 = 3 W, R3 = 4W.
There are 2 voltmeters:
1 reads the 4 W & 1 reads the 2 W bulb.
2 ammeters - 1 reads the total current 1
reads the current in the 3 W branch.
A. Sketch the circuit. Find the power in each.
B. What is relative brightness?
C. Add a 100 W bulb to the circuit &
calculate the power in each. What
happens to the brightness? What
happens to the total current?
D. What if the 2W is removed? What
happens to the brightness of the
remaining bulbs?
Use of Meters
Ammeters measure current so circuit
current must flow through meter.
Connect meter in series to measure
current.
Ideal ammeter has zero resistance.
• What do you think will happen if an
ammeter is connected in parallel by
accident?
Voltmeters measure p.d. across
resistors so must be connected in
parallel.
Ideal voltmeter has infinite
resistance.
• What do you think will happen if a
voltmeter is connected in series by
accident?
Kirchoff’s Laws
The current entering junction = current
exiting. Application of “conservation of
charge”.
Total Voltage = sum of all partial voltages
on circuit. Application of conservation of
energy.
6V
2V
4V
What is the current in the other wire?
10 A
4A
?
16 A
2A
What is the current in the unknown
wire?
4A
2A
6A
?
12A
Fuses – appliances are rated for the
power they can safely dissipate.
That implies a certain current & voltage
(power).
Fuses should be chosen to have a current
rating a bit higher than the one for
which the resistor is designed.
Should fuses and circuit breakers be
connected in parallel or in series?
Why?
If a 60 W bulb is connected to a 120 V
source, the current is:
P = VI
I=
I = P/V.
60 J/s = 0.5 C/s .5A.
120 J/C
Fuse should be ~ .6-1 A.