Transcript Direct Current Circuits

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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
-Potentiometer
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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
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1- Sources of emf
 The source that maintains the current in a closed
circuit is called a source of emf
 Any devices that increase the potential energy of
charges circulating in circuits are sources of emf
 Examples include batteries and generators
 SI units are Volts
 The emf is the work done per unit charge
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emf and Internal Resistance
 A real battery has
some internal
resistance “r”
 Therefore, the
terminal voltage is
not equal to the emf
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More About Internal Resistance
 The schematic shows the
internal resistance, r
 The terminal voltage is
ΔV = Vb-Va
 ΔV = ε – Ir
 For the entire circuit,
ε = IR + Ir
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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
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Internal Resistance and emf, cont
 ε is equal to the terminal voltage when the
current is zero
 Also called the open-circuit voltage
 R is called the load resistance
 The current depends on both the resistance external
to the battery and the internal resistance
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Internal Resistance and emf, final
 When R >> r, r can be ignored
 Generally assumed in problems
 Power relationship
 I e = I2 R + I2 r

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When R >> r, most of the power
delivered by the battery is
transferred to the load resistor
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Quiz 1
 In 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.
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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.
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2-Resistors in Series
 When two or more resistors are connected end-toend, they are said to be in series
 The 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
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Resistors in Series, cont
 Potentials 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
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Equivalent Resistance – Series
 Req = 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
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Equivalent Resistance – Series:
An Example
 Four resistors are replaced with their equivalent
resistance
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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.
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(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.
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Resistors in Parallel
 The 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
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Equivalent Resistance – Parallel,
Example:
 Equivalent resistance replaces the two original resistances
 Household circuits are wired so the electrical devices
are connected in parallel
 Circuit breakers may be used in series with other circuit
elements for safety purposes
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Equivalent Resistance – Parallel
 Equivalent Resistance
1
1
1
1




R eq R1 R 2 R 3
 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
The equivalent is always less than
the smallest resistor in the group
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Problem-Solving Strategy, 1
 Combine all resistors in series
 They carry the same current
 The potential differences across them are not
the same
 The resistors add directly to give the equivalent
resistance of the series combination:
Req = R1 + R2 + …
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Problem-Solving Strategy, 2
 Combine all resistors in parallel
 The potential differences across them are the
same
 The currents through them are not the same
 The equivalent resistance of a parallel
combination is found through reciprocal
addition:
1
1
1
1




R eq R1 R 2 R 3
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Problem-Solving Strategy, 3
A complicated circuit consisting of several resistors and
batteries can often be reduced to a simple circuit with
only one resistor
 Replace any resistors in series or in parallel using
steps 1 or 2.
 Sketch the new circuit after these changes have been
made
 Continue to replace any series or parallel
combinations
 Continue until one equivalent resistance is found
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Problem-Solving Strategy, 4
 If 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 2
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Equivalent Resistance
–
Complex Circuit
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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.
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(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.
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More About the Junction Rule
 I1 = I2 + I3
 From Conservation of
Charge
 Diagram b shows a
mechanical analog
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Setting Up Kirchhoff’s Rules
 Assign symbols and directions to the currents in
all branches of the circuit
 If 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 loop
 Record voltage drops and rises as they occur
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More About the Loop Rule
 Traveling 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
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Loop Rule, final
 In (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
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Junction Equations from Kirchhoff’s
Rules
 Use 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 equation
 In general, the number of times the
junction rule can be used is one fewer than
the number of junction points in the circuit
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Loop Equations from Kirchhoff’s
Rules
 The 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
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Example:
 (A) Find the current in the circuit.
starting at a, we see that a b
represents a potential difference
of + Ɛ1
b  c represents a potential
difference of -IR1,
c  d represents a potential
difference of - Ɛ2, and
d  a represents a potential
difference of -IR2
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The negative sign for I indicates that the direction of the current is
opposite the assumed direction.
(B) What power is delivered to each resistor? What
power is delivered by the 12-V battery?
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Example:
Voltage vs. current graph of a conductor is given below. Find the change in the
resistance of conductor in first and third intervals.
 We use ohm's law to find relation between V, I
and R. ( V= I R)
 Interval I: Since potential and current increase
linearly, resistance of the conductor becomes
constant.
 Interval II: In this interval, potential is constant
but current increases. Thus, resistance of the
conductor must decrease to make potential
constant.
 Interval III: In this interval potential
increases but current is constant. Thus,
resistance of the conductor must increase to
make potential increase.
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