Transcript Current, pd, resistor combinations, potential dividers File

Properties of Current
Current must flow in a
complete circuit - current
cannot be “lost” anywhere.
Kirchoff’s point rule - the
current flowing into any
point or component must be
equal to the current flowing
out of it.
Properties of Current
Components in series
must have the same
current flowing through
them.
Properties of Current
For components in
parallel, the current is
split between them.
Water
splitter
analogy
Properties of
Current
Components in series
must have the same
current flowing through
them.
For components in
parallel, the current is
split between them.
Car tollgate analogy:
Properties of Current
Current must flow in a
complete circuit - current
cannot be “lost” anywhere.
Kirchoff’s point rule - the
current flowing into any
point or component must be
equal to the current flowing
out of it.
Components in series must
have the same current
flowing through them.
For components in parallel,
the current is split between
them.
Properties of p.d.
The electric field is
conservative so the
potential at a given
point is independent of
the route taken.
Kirchoff’s loop rule –
the sum of potential
differences around a
closed loop must be
zero.
V4+V1=V3+V2
V3+V2+V1+V4=0
Gravitational analogy
Properties of p.d.
For a simple circuit, the sum
of potential differences is
equal and opposite to the
e.m.f. of the power supply.
The mechanism lifting marbles is analogous to e.m.f.
The rest of the circuit is similar to the rolling down part of this toy.
From the law of energy conservation: the work of the mechanism is equal
to the energy the marble has on top. This is similar to the law that the
e.m.f is equal to the potential difference in the circuit.
Properties of p.d.
If a circuit branches, the p.d.
across each branch is the same
and is not split.
V2-V3=0 (from the red loop)
emf=V1+V2 (from the blue loop)
Similar to a waterfall: all water
streams deliver the same energy
Properties of p.d.
The electric field is
conservative so the potential
at a given point is
independent of the route
taken.
Kirchoff’s loop rule – the
sum of potential differences
around a closed loop must
be zero.
For a simple circuit, the sum
of potential differences is
equal and opposite to the
e.m.f. of the power supply.
If a circuit branches, the p.d.
across each branch is the
same and is not split.
Resistors in Series and Parallel
V1
I2
I1
V2 Why do resistances of two
resistors in series add?
A
Rtotal
R total
V
 R1  R 2
Consider the first Kirchoff’s law
for node A
I2
I1
A
For two resistors in series,
the resistances add.
I1=I2=I
Consider the second Kirchoff’s
law for the green loop
V1+V2=V
Resistors in Series and Parallel
V1
I2
I1
A
Rtotal
R total
V
 R1  R 2
V2
From Kirchoff’s Laws
V1+V2=V
I1=I2=I
Ohm’s Law
V1=I1R1=IR1;
V2=I2R2=IR2
Since V1+V2=V we have:
V=IR1+IR2=I(R1+R2)
For two resistors in series,
the resistances add.
The same is true of three,
four, five...resistances
Ohm’s Law:
Rtotal =V/I=I(R1+R2)/I
Rtotal = R1+R2
Resistors in Series and Parallel
I
I1
I2
A
B
I1
I2
I
Rtotal
1
1
1


R total R1 R 2
For two resistors in parallel,
the resistances add in
reciprocal to give the
reciprocal resistance.
Why do resistances of two
resistors in parallel add in
reciprocal?
Consider the first Kirchoff’s law
for node A: I=I1+I2
I
I1
I2 A
Resistors in Series and Parallel
V1
I
I1
I2
B
A
I1
I2
I
V2
1
R total
1
1 Rtotal


R1 R 2
For two resistors in parallel,
the resistances add in
reciprocal to give the
reciprocal resistance.
The same is true of three,
four, five...resistances
Why resistances of two
resistors in parallel add in
reciprocal?
Consider the first Kirchoff’s law
for node A: I=I1+I2
I
I1
I2 A
Consider the second Kirchoff’s
law for the green loop
V1-V2=0
V1=V2
Resistors in Series and Parallel
V1
I
I1
I2
From Kirchoff’s laws:
B
A
I1
I2
I
V2
1
R total
1
1 Rtotal


R1 R 2
For two resistors in parallel,
the resistances add in
reciprocal to give the
reciprocal resistance.
The same is true of three,
four, five...resistances
I=I1+I2 ; V1=V2 =V
From Ohm’s Law
I1=V1 /R1= V/R1;
I2=V2 /R2 =V/R2;
Therefore,
I=I1+I2= V/R1 + V/R2
= V(1/R1 +1/R2 )
From Ohm’s Law
I= V/Rtotal
1
1
1


R total R 1 R 2
Resistors in Series and Parallel
Rtotal
1
R total  R 1  R 2
For two resistors in series,
the resistances add.
The same is true of three,
four, five...resistances
R total
Rtotal
1
1


R1 R 2
For two resistors in parallel,
the resistances add in
reciprocal to give the
reciprocal resistance.
The same is true of three,
four, five...resistances
More complicated circuits
1/Rt1=1/56+1/33 = 0.018+0.03
= 0.048 1/Ohm
Rt1=20.8 Ohm
Rtotal=20.8 Ohm +47 Ohm = 67.8 Ohm
Solving a complex resistor network
E = 15V
2Ω
A
9Ω
A Point B
3Ω
Point A
6Ω
15 Ω
3Ω
2Ω
10 Ω
Point C
A
5Ω
Using Ohm’s Law and the rules for combining resistors, calculate the current flowing
through the ammeters at points A, B and C
Potential Divider
Vout
If a voltage supply is connected
across two resistors in series, then
we have a potential divider.
V1
R1
in
R2
V1
Vin
V2
Potential Divider
The current in the circuit
I=Vin/Rtotal
Since our resistors are in
series, thus, Rtotal=R1+R2
From Ohm’s law:
I
I=Vin/(R1+R2)
From Ohm’s law:
Vout=V1=IR1; V2=IR2
The potential difference across
each one is proportional to the
resistance.
V R
V1  Vout 
in
1
R1  R2 
Vout
in
Vin R2
V2 
R1  R2 
Even if we have a battery producing voltage Vin, we also can
generate any voltage lower Vin by using a potential divider
Battery
Any real voltage source has
an internal resistance, so
whenever it is connected to a
real load there is a potential
divider effect.
Battery
Any real voltage source has an internal
resistance, so whenever it is connected to a
real load there is a potential divider effect.
Internal resistance Ri and Resistance of a
load are in series, thus, total resistance
Rtotal=R+Ri
Current in the circuit is I=E/(Rtotal) with E
being the e.m.f of the battery
Voltage produced by the battery is
V=RI=E(R/Rtotal)
Potential Divider
If a voltage supply is connected
across two resistors in series, then
we have a potential divider.
The potential difference across
each one is proportional to the
resistance.
VR1
V1 
R1  R 2 
VR 2
V2 
R1  R 2 
Any real voltage source has an
internal resistance, so whenever it
is connected to a real load there is
a potential divider effect.