Download Curent, Resistance ,Direct-current Circuits

Current, Resistance,
Direct-current Circuits
1. Electric current
 The current is the rate at which
charge flows through this surface
 Suppose ΔQ is the amount of charge
that flows through an area A in a
time interval Δt and that the
direction of flow is perpendicular to
the area. Then the current I is equal
to the amount of charge divided by
the time
 I= Δ Q/Δt
 SI C/s=A
(Ampere)
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2. Current and voltage
measuraments in circuits
3. Resistance and Ohm’s Law
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Resistance is the ratio of the
voltage across the conductor to
the current:
R = ΔV/ I
SI units :1V/A=1Ω (Ohms)
Ohm’s Law: the resistance remains
constant over a wide range of
applied voltage or currents:
ΔV =IR
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A resistor : is a conductor that
provides a specified resistance in an
electric circuit
The resistance is proportional to the
conductor’s length l and inversely
proportional to its cross-sectional
area A:
R =ρ l/A
ρ –resistivity of the material (ct. of
proportionality) SI unit: Ω m
4. Electrical energy and power
 The rate at which the system loses
potential energy as the charge passes
through resistor is equal to the rate at
which the system gains internal energy in
the resistor.
 (ΔQ/ Δt) ΔV =I ΔV
 Power P - the rate at which energy is
delivered to the resistor:
 P =I ΔV
2
2
 P =I R = ΔV /R
 SI: kilowatt-hour
 1kWh =(103W)(3600s) =3.6x106J
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Question: Some homes have light
dimmers that are operated by
rotating a knob. What is being
changed in the electric circuit when
the know is rotated?
R
I
Direct-Current Circuits
5. Sources of EMF (electromotive
force)- a “ charge pump” that forces
electrons to move in a direction
opposite the electrostatic field inside
the source
 The emf ε of a source is the work
done per unit charge (SI unit: V)
 ΔV =ε –Ir
 ε = the terminal voltage when the
current is zero (open circuit voltage)
ΔV= IR
(R- the external resistance)
 ε =IR +Ir;
 I = ε / (R+r)
 I ε =I2R + I2r if r<<R
 (the power delivered
 by the battery is
 transferred to the load
 resistance)
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6. Resistors in series
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ΔV = IR1 +IR2 =I(R1+R2)
ΔV = I Req
IReq = I(R1+R2)
Req =R1+R2
Req =R1+R2+….
The equivalent resistance of a series
combination of resistors is the
algebraic sum of the individual
resistances and is always greater
than any individual resistance
7. Resistors in parallel
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The potential differences across resistors
are the same because each is connected
directly across the battery terminals
Because charge is conserved, the current I
that enters point a must equal the total
current I1+I2 leaving that point
I =I1+I2
I1=ΔV /R1 ;
I2=ΔV /R2 ;
I =ΔV /Req ;
1/Req = 1/R1 +1/R2
The inverse of the equivalent resistance of
two or more resistors connected in parallel
is the sum of the inverses of the individual
resistances and is always less than the
smallest resistance in the group
8. KiRchhOff’s RuLes:
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1. The sum of the currents entering
any jonction must equal the sum of
the currents leaving that junction
(junction rule)
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2. The sum of the potential
differences across all the elements
around any closed circuit loop must
be zero (loop rule)
a) if the resistor is traversed in the direction
of the current, the charge in electric
potential across the resistor is –IR
b) If a resistor is traversed in the direction
opposite the current, the charge in electric
potential across resistors is +IR
c) if a source of emf is traversed in the
direction of the emf (from – to +) the
charge in electric potential is +Σ
d) if a source of emf is traversed in the
direction opposite the emf, the charge in
electric potential is -Σ
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Problem solving strategy:
1. Assign labels and symbols to all the
known and unknown quantities
2. Assign directions to the currents in each
part of the circuit
3. Apply the junction rule to any junction
in the circuit
4. Apply Kirchhoff’s loop rule, to as many
loops in the circuit as are needed to solve
for the unknowns
5. solve the equations
6. Check your answers by substituting
them into the original equations
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Problem: Find the currents in the
circuit shown in fig. by using
Kirchhoff’s rules
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9. RC circuits
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We consider that the capacitor is initially
uncharged with the switch open. After the
switch is closed, the battery begins to
charge the plates of capacitor and the
charge passes through resistor
A the capacitor is being charged, the
circuit carries a changing current. The
process continues until the capacitor is
charged to a maximum value
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Q=Cε
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ε -maximum voltage across the capacitor
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Once the capacitor is fully charged, the current
in circuit is zero
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q=Q(1-e –t/RC)
RC=σ –time constant
The time constant represents the
time required for the charge to
increase from zero to 63.2% its
maximum equilibrium value
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Before the switch is closed the potential
difference across the charged capacitor is
Q/C
Once the switch is closed, the charge
begins to flow through the resistor, until
the capacitor is fully charged
q=Qe-t/RC
The charge decreasses exponentially with
time
ΔV=εe-t/RC