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Direct Current Circuits:
3-1 EMF
3-2 Resistance in series and parallel .
3-3 Kirchhoff’s Rules 3-4 RC circuit
3-5 Electrical instruments
- Weston bridge
-Potentiometer19-11-2014 2FCI
Objectives:Defined some circuits in which resistors
can be combined using simple rules.
Understand the analysis of more complicated circuits is simplified using two rules known as Kirchhoff’s rules.
Describe electrical meters for measuring current and potential difference
19-11-2014 3FCI
1- Sources of emfThe source that maintains the current in a
closed circuit is called a source of emfAny devices that increase the potential
energy of charges circulating in circuits are sources of emf
Examples include batteries and generators
SI units are VoltsThe emf is the work done per unit charge
19-11-2014 4FCI
emf and Internal ResistanceA real battery has
some internal resistance “r”
Therefore, the terminal voltage is not equal to the emf
19-11-2014 5FCI
More About Internal ResistanceThe schematic shows
the internal resistance, r
The terminal voltage is ΔV = Vb-Va
ΔV = ε – IrFor the entire
circuit,
ε = IR + Ir
19-11-2014 6FCI
Now imagine moving through the
battery from a to b and measuring
the electric potential at various
locations. As we pass from the
negative terminal to the positive
terminal, the potential increases by
an amount Ɛ. As we move through
the resistance r, the potential
decreases by an amount Ir. Constant
potential from b to c. As we move
through the resistance R, the
potential decreases by an amount IR
19-11-2014 7FCI
Internal Resistance and emf, contε is equal to the terminal voltage
when the current is zero
Also called the open-circuit voltageR is called the load resistance
The current depends on both the resistance external to the battery and the internal resistance
19-11-2014 8FCI
Internal Resistance and emf, finalWhen R >> r, r can be ignored
Generally assumed in problemsPower relationship
I = I2 R + I2 rWhen R >> r, most of the power delivered by the battery is transferred to the load resistor
19-11-2014 9FCI
Quiz 1In order to maximize the percentage of the
power that is delivered from a battery to a device, the internal resistance of the battery should be:
(a) as low as possible (b) as high as possible (c) The percentage does not depend on the internal resistance.
19-11-2014 10FCI
Example 1:
A battery has an emf of 12.0 V and an internal resistance of 0.05 Ω. Its terminals are connected to a load resistance of 3.00 Ω.
(A) Find the current in the circuit and the terminal voltage of the battery.
(B) Calculate the power delivered to the load resistor, the power delivered to the internal resistance of the battery, and the power delivered by the battery.
19-11-2014 11FCI
2-Resistors in SeriesWhen two or more resistors are connected
end-to-end, they are said to be in seriesThe current is the same in all resistors
because any charge that flows through one resistor flows through the other
The sum of the potential differences across the resistors is equal to the total potential difference across the combination
19-11-2014 12FCI
Resistors in Series, contPotentials add
ΔV = IR1 + IR2 = I (R1+R2)
Consequence of Conservation of Energy
The equivalent resistance has the effect on the circuit as the original combination of resistors
19-11-2014 13FCI
Equivalent Resistance – SeriesReq = R1 + R2 + R3 + …
The equivalent resistance of a series combination of resistors is the algebraic sum of the individual resistances and is always greater than any of the individual resistors
19-11-2014 14FCI
Equivalent Resistance – Series: An Example
Four resistors are replaced with their equivalent resistance
19-11-2014 15FCI
Quiz 2:With the switch in the circuit of Fig. A closed, there is no
current in R2, because the current has an alternate zero-resistance path through the switch. There is current in R1 and this current is measured with the ammeter, at the right side of the circuit. If the switch is opened (Fig. B), there is current in R2 . What happens to the reading on the ammeter when the switch is opened? (a) the reading goes up; (b) the reading goes down; (c) the reading does not change.
19-11-2014 16FCI
(b). When the switch is opened, resistors
R1 and R2 are in series, so that the
total circuit resistance is larger than
when the switch was closed. As a
result, the current decreases.
19-11-2014 17FCI
Resistors in ParallelThe potential difference across each resistor
is the same because each is connected directly across the battery terminals
The current, I, that enters a point must be equal
to the total current leaving that point
I = I1 + I2
The currents are generally not the same
Consequence of Conservation of Charge
19-11-2014 18FCI
Equivalent Resistance – Parallel, Example:
Equivalent resistance replaces the two original resistances
Household circuits are wired so the electrical devices are connected in parallelCircuit breakers may be used in series with other
circuit elements for safety purposes19-11-2014 19FCI
Equivalent Resistance – ParallelEquivalent Resistance
The inverse of the equivalent resistance of two or more resistors connected in parallel is the algebraic sum of the inverses of the individual resistance
321eq R
1
R
1
R
1
R
1
The equivalent is always less than the smallest resistor in the group
19-11-2014 20FCI
Problem-Solving Strategy, 1Combine all resistors in series
They carry the same currentThe potential differences across them
are not the sameThe resistors add directly to give the
equivalent resistance of the series combination:
Req = R1 + R2 + …
19-11-2014 21FCI
Problem-Solving Strategy, 2
Combine all resistors in parallelThe potential differences across them
are the sameThe currents through them are not
the sameThe equivalent resistance of a
parallel combination is found through reciprocal addition:
321eq R
1
R
1
R
1
R
1
19-11-2014 22FCI
Problem-Solving Strategy, 3
A complicated circuit consisting of several resistors and batteries can often be reduced to a simple circuit with only one resistorReplace any resistors in series or in parallel
using steps 1 or 2. Sketch the new circuit after these changes
have been madeContinue to replace any series or parallel
combinations Continue until one equivalent resistance is
found19-11-2014 23FCI
Problem-Solving Strategy, 4If the current in or the potential difference
across a resistor in the complicated circuit is
to be identified, start with the final circuit
found in step 3 and gradually work back
through the circuits
Use ΔV = I R and the procedures in
steps 1 and 219-11-2014 24FCI
Quiz 3:With the switch in the circuit of Fig. A
open, there is no current in R2. There is current in R1 and this current is measured with the ammeter at the right side of the circuit. If the switch is closed Fig.B, there is current in R2. What happens to the reading on the ammeter when the switch is closed?
(a) the reading goes up; (b) the reading goes down; (c) the reading does not change.19-11-2014 26FCI
(a). When the switch is closed, resistors R1
and R2 are
in parallel, so that the total circuit
resistance is smaller than when the switch
was open. As a result, the current
increases.
19-11-2014 27FCI
More About the Junction RuleI1 = I2 + I3
From Conservation of Charge
Diagram b shows a mechanical analog
19-11-2014 28FCI
Setting Up Kirchhoff’s Rules
Assign symbols and directions to the currents in all branches of the circuitIf a direction is chosen incorrectly, the
resulting answer will be negative, but the magnitude will be correct
When applying the loop rule, choose a direction for transversing the loopRecord voltage drops and rises as they
occur
19-11-2014 29FCI
More About the Loop RuleTraveling around the loop
from a to b
In (a), the resistor is transversed in the direction of the current, the potential across the resistor is –IR
In( b), the resistor is transversed in the direction opposite of the current, the potential across the resistor is +IR
19-11-2014 30FCI
Loop Rule, finalIn (c), the source of emf is
transversed in the direction of the emf (from – to +), the change in the electric potential is +ε
In (d), the source of emf is transversed in the direction opposite of the emf (from + to -), the change in the electric potential is -ε
19-11-2014 31FCI
Junction Equations from Kirchhoff’s RulesUse the junction rule as often as needed,
so long as, each time you write an equation, you include in it a current that has not been used in a previous junction rule equationIn general, the number of times the junction rule can be used is one fewer than the number of junction points in the circuit
19-11-2014 32FCI
Loop Equations from Kirchhoff’s RulesThe loop rule can be used as often as needed
so long as a new circuit element (resistor or battery) or a new current appears in each new equation
You need as many independent equations as you have unknowns
19-11-2014 33FCI
Example: (A) Find the current in the circuit.
starting at a, we see that a b represents a potential differenceof + Ɛ1
b c represents a potential difference of -IR1, c d represents a potential difference of - Ɛ2, andd a represents a potential difference of -IR2
19-11-2014 34FCI
(B) What power is delivered to each resistor? What power is delivered by the 12-V battery?
The negative sign for I indicates that the direction of the
current is opposite the assumed direction.
19-11-2014 35FCI