Download Circuits in “Real life”

Digital Multimeters
Non-Ideal Behaviors...
Circuits in “Real life”
PHYS 272 - David Blasing
Monday July 20th, 2015
PHYS 272 - David Blasing
Matter and Interactions: 20.1 - 20.7
Digital Multimeters
Non-Ideal Behaviors...
Our “Road Map”
2/21
PHYS 272 - David Blasing
Matter and Interactions: 20.1 - 20.7
Digital Multimeters
Non-Ideal Behaviors...
Brief review of last lecture
Effective capacitance for capacitors in series
P 1
1
N CN
Ceff =
Effective capacitance for capacitors in parallel
P
Ceff = N CN
The fringe field’s roles:
In a charging capacitor, it grows until it stops the current flow. In
a discharging capacitor, it drives the current which discharges the
capacitor.
but there is more...
3/21
PHYS 272 - David Blasing
Matter and Interactions: 20.1 - 20.7
Digital Multimeters
Non-Ideal Behaviors...
Brief review of last lecture
Charging a capacitor
t
Q(t) = C (EMF )(1 − e − RC )
Discharging a charged capacitor
t
Q(t) = C (EMF )e − RC
Potential energy of a charged capacitor
U = 21 CV 2
4/21
PHYS 272 - David Blasing
Matter and Interactions: 20.1 - 20.7
Digital Multimeters
Non-Ideal Behaviors...
Voltmeter/Ammeter
Ammeters/Capacitance
Digital Multimeters
A Digital Multimeter (like the ones that you
use in lab), a “DMM,” is super useful
5/21
PHYS 272 - David Blasing
Matter and Interactions: 20.1 - 20.7
Digital Multimeters
Non-Ideal Behaviors...
Voltmeter/Ammeter
Ammeters/Capacitance
Digital Multimeters
A Digital Multimeter (like the ones that you
use in lab), a “DMM,” is super useful
The most common things they measure are:
1
2
3
4
Voltage (as a “voltmeter”)
Amps (as an “ammeter”)
Resistance (as an “ohmmeter”)
Capacitance
5/21
PHYS 272 - David Blasing
Matter and Interactions: 20.1 - 20.7
Digital Multimeters
Non-Ideal Behaviors...
Voltmeter/Ammeter
Ammeters/Capacitance
Digital Multimeters
A Digital Multimeter (like the ones that you
use in lab), a “DMM,” is super useful
The most common things they measure are:
1
2
3
4
Voltage (as a “voltmeter”)
Amps (as an “ammeter”)
Resistance (as an “ohmmeter”)
Capacitance
Typically an electrical property of a circuit is
of interest, but the DMM’s presence alters
the circuit...this is actually an annoying
problem in experimental physics
5/21
PHYS 272 - David Blasing
Matter and Interactions: 20.1 - 20.7
Digital Multimeters
Non-Ideal Behaviors...
Voltmeter/Ammeter
Ammeters/Capacitance
Voltmeter
As a voltmeter, a DMM typically contains a
sophisticated “comparator” circuit which
compares voltage on its terminals to an
internal reference voltage
How can a DMM measure voltage without
disturbing a circuit too much?
6/21
PHYS 272 - David Blasing
Matter and Interactions: 20.1 - 20.7
Digital Multimeters
Non-Ideal Behaviors...
Voltmeter/Ammeter
Ammeters/Capacitance
Voltmeter
As a voltmeter, a DMM typically contains a
sophisticated “comparator” circuit which
compares voltage on its terminals to an
internal reference voltage
How can a DMM measure voltage without
disturbing a circuit too much?
The effective (“net”) resistance of the
circuit is just R1
6/21
PHYS 272 - David Blasing
Matter and Interactions: 20.1 - 20.7
Digital Multimeters
Non-Ideal Behaviors...
Voltmeter/Ammeter
Ammeters/Capacitance
Voltmeter
As a voltmeter, a DMM typically contains a
sophisticated “comparator” circuit which
compares voltage on its terminals to an
internal reference voltage
How can a DMM measure voltage without
disturbing a circuit too much?
The effective (“net”) resistance of the
circuit is just R1
The effective (“net”) resistance of the lower
circuit is R1 + R2
6/21
PHYS 272 - David Blasing
Matter and Interactions: 20.1 - 20.7
Digital Multimeters
Non-Ideal Behaviors...
Voltmeter/Ammeter
Ammeters/Capacitance
Voltmeter
As a voltmeter, a DMM typically contains a
sophisticated “comparator” circuit which
compares voltage on its terminals to an
internal reference voltage
How can a DMM measure voltage without
disturbing a circuit too much?
The effective (“net”) resistance of the
circuit is just R1
The effective (“net”) resistance of the lower
circuit is R1 + R2
If R2 R1 , Reff → R1 ; the circuit is
approximately undisturbed
6/21
PHYS 272 - David Blasing
Matter and Interactions: 20.1 - 20.7
Digital Multimeters
Non-Ideal Behaviors...
Voltmeter/Ammeter
Ammeters/Capacitance
Voltmeters
Voltmeters must have high internal resistance (typically ≈ 10MΩs)
and must be placed in parallel with the circuit element of interest
They are good for measuring voltages on circuit elements with
resistance of ≈ 100KΩs or so.
PHYS 272 - David Blasing
Matter and Interactions: 20.1 - 20.7
7/21
Digital Multimeters
Non-Ideal Behaviors...
Voltmeter/Ammeter
Ammeters/Capacitance
Ammeters
As an ammeter, a DMM typically uses it’s
voltmeter circuit in parallel with an internal
resistor of a known value
How can a DMM measure the current in a
circuit without disturbing it much?
8/21
PHYS 272 - David Blasing
Matter and Interactions: 20.1 - 20.7
Digital Multimeters
Non-Ideal Behaviors...
Voltmeter/Ammeter
Ammeters/Capacitance
Ammeters
As an ammeter, a DMM typically uses it’s
voltmeter circuit in parallel with an internal
resistor of a known value
How can a DMM measure the current in a
circuit without disturbing it much?
The effective (“net”) resistance of the
circuit is just R1
8/21
PHYS 272 - David Blasing
Matter and Interactions: 20.1 - 20.7
Digital Multimeters
Non-Ideal Behaviors...
Voltmeter/Ammeter
Ammeters/Capacitance
Ammeters
As an ammeter, a DMM typically uses it’s
voltmeter circuit in parallel with an internal
resistor of a known value
How can a DMM measure the current in a
circuit without disturbing it much?
The effective (“net”) resistance of the
circuit is just R1
The effective (“net”) resistance of the lower
circuit is R1 + R2
8/21
PHYS 272 - David Blasing
Matter and Interactions: 20.1 - 20.7
Digital Multimeters
Non-Ideal Behaviors...
Voltmeter/Ammeter
Ammeters/Capacitance
Ammeters
As an ammeter, a DMM typically uses it’s
voltmeter circuit in parallel with an internal
resistor of a known value
How can a DMM measure the current in a
circuit without disturbing it much?
The effective (“net”) resistance of the
circuit is just R1
The effective (“net”) resistance of the lower
circuit is R1 + R2
If R2 R1 , Reff → R1 ; the circuit is
approximately undisturbed
8/21
PHYS 272 - David Blasing
Matter and Interactions: 20.1 - 20.7
Digital Multimeters
Non-Ideal Behaviors...
Voltmeter/Ammeter
Ammeters/Capacitance
Ammeters
Ammeters must have low internal resistance (typically ≈ .5Ωs) and
must be placed in series with the circuit element of interest
Ammeters reliably measure currents:
through circuits with resistance of ≈ 10Ωs or more
use their voltmeter circuitry in parallel with a small internal
resistor
9/21
PHYS 272 - David Blasing
Matter and Interactions: 20.1 - 20.7
Digital Multimeters
Non-Ideal Behaviors...
Voltmeter/Ammeter
Ammeters/Capacitance
Ohmmeter
As an ohmmeter, a DMM typically drives a
small, fixed current
10/21
PHYS 272 - David Blasing
Matter and Interactions: 20.1 - 20.7
Digital Multimeters
Non-Ideal Behaviors...
Voltmeter/Ammeter
Ammeters/Capacitance
Ohmmeter
As an ohmmeter, a DMM typically drives a
small, fixed current
The DMM measures the ∆V required to
drive that current through the circuit
element being measured
10/21
PHYS 272 - David Blasing
Matter and Interactions: 20.1 - 20.7
Digital Multimeters
Non-Ideal Behaviors...
Voltmeter/Ammeter
Ammeters/Capacitance
Ohmmeter
As an ohmmeter, a DMM typically drives a
small, fixed current
The DMM measures the ∆V required to
drive that current through the circuit
element being measured
DMM measures that change in potential,
and R = ∆V
I
10/21
PHYS 272 - David Blasing
Matter and Interactions: 20.1 - 20.7
Digital Multimeters
Non-Ideal Behaviors...
Voltmeter/Ammeter
Ammeters/Capacitance
Ohmmeter
As an ohmmeter, a DMM typically drives a
small, fixed current
The DMM measures the ∆V required to
drive that current through the circuit
element being measured
DMM measures that change in potential,
and R = ∆V
I
Ohmmeter needs to be hooked up in parallel
while there are no other voltages present
10/21
PHYS 272 - David Blasing
Matter and Interactions: 20.1 - 20.7
Digital Multimeters
Non-Ideal Behaviors...
Voltmeter/Ammeter
Ammeters/Capacitance
Capacitance
DMMs can measure capacitance in series
11/21
PHYS 272 - David Blasing
Matter and Interactions: 20.1 - 20.7
Digital Multimeters
Non-Ideal Behaviors...
Voltmeter/Ammeter
Ammeters/Capacitance
Capacitance
DMMs can measure capacitance in series
Apply a current to circuit element being
tested, and measure ∆V at different times
11/21
PHYS 272 - David Blasing
Matter and Interactions: 20.1 - 20.7
Digital Multimeters
Non-Ideal Behaviors...
Voltmeter/Ammeter
Ammeters/Capacitance
Capacitance
DMMs can measure capacitance in series
Apply a current to circuit element being
tested, and measure ∆V at different times
−1
From the definition, C = I ( dV
dt )
11/21
PHYS 272 - David Blasing
Matter and Interactions: 20.1 - 20.7
Digital Multimeters
Non-Ideal Behaviors...
Voltmeter/Ammeter
Ammeters/Capacitance
Clicker Question 1
12/21
PHYS 272 - David Blasing
Matter and Interactions: 20.1 - 20.7
Digital Multimeters
Non-Ideal Behaviors...
Voltmeter/Ammeter
Ammeters/Capacitance
Clicker Question 2
13/21
PHYS 272 - David Blasing
Matter and Interactions: 20.1 - 20.7
Digital Multimeters
Non-Ideal Behaviors...
Voltmeter/Ammeter
Ammeters/Capacitance
Clicker Question 3
14/21
PHYS 272 - David Blasing
Matter and Interactions: 20.1 - 20.7
Digital Multimeters
Non-Ideal Behaviors...
Batteries
Ohmic and non-ohmic
Batteries in real-life
Ideal battery behavior includes:
1
Produces its constant EMF always
2
Has no internal resistance
3
Can source any amount of current
That said, everybody knows that batteries in real-life get hot...so
15/21
PHYS 272 - David Blasing
Matter and Interactions: 20.1 - 20.7
Digital Multimeters
Non-Ideal Behaviors...
Batteries
Ohmic and non-ohmic
Batteries in real-life
Ideal battery behavior includes:
1
Produces its constant EMF always
2
Has no internal resistance
3
Can source any amount of current
That said, everybody knows that batteries in real-life get hot...so
they have internal resistance
15/21
PHYS 272 - David Blasing
Matter and Interactions: 20.1 - 20.7
Digital Multimeters
Non-Ideal Behaviors...
Batteries
Ohmic and non-ohmic
Batteries internal resistance
Our previous model of a battery:
Better model of a battery:
Notes:
16/21
PHYS 272 - David Blasing
Matter and Interactions: 20.1 - 20.7
Digital Multimeters
Non-Ideal Behaviors...
Batteries
Ohmic and non-ohmic
Batteries internal resistance
Our previous model of a battery:
Better model of a battery:
Notes:
1
EMF is still constant (though it decreases as the battery dies)
16/21
PHYS 272 - David Blasing
Matter and Interactions: 20.1 - 20.7
Digital Multimeters
Non-Ideal Behaviors...
Batteries
Ohmic and non-ohmic
Batteries internal resistance
Our previous model of a battery:
Better model of a battery:
Notes:
1
EMF is still constant (though it decreases as the battery dies)
2
∆Vbatt = EMF -rint I
16/21
PHYS 272 - David Blasing
Matter and Interactions: 20.1 - 20.7
Digital Multimeters
Non-Ideal Behaviors...
Batteries
Ohmic and non-ohmic
Batteries internal resistance
Our previous model of a battery:
Better model of a battery:
Notes:
1
EMF is still constant (though it decreases as the battery dies)
2
∆Vbatt = EMF -rint I
3
If I=0, ∆Vbatt =EMF (can be measured with a voltmeter)
16/21
PHYS 272 - David Blasing
Matter and Interactions: 20.1 - 20.7
Digital Multimeters
Non-Ideal Behaviors...
Batteries
Ohmic and non-ohmic
Batteries internal resistance
Our previous model of a battery:
Better model of a battery:
Notes:
1
EMF is still constant (though it decreases as the battery dies)
2
∆Vbatt = EMF -rint I
3
If I=0, ∆Vbatt =EMF (can be measured with a voltmeter)
4
If I6=0, ∆Vbatt <EMF (can be measured with a voltmeter)
16/21
PHYS 272 - David Blasing
Matter and Interactions: 20.1 - 20.7
Digital Multimeters
Non-Ideal Behaviors...
Batteries
Ohmic and non-ohmic
Batteries internal resistance
Our previous model of a battery:
Better model of a battery:
Notes:
1
EMF is still constant (though it decreases as the battery dies)
2
∆Vbatt = EMF -rint I
3
If I=0, ∆Vbatt =EMF (can be measured with a voltmeter)
4
If I6=0, ∆Vbatt <EMF (can be measured with a voltmeter)
5
∆Vbatt drives current in circuits, so in this model batteries
can source only a finite amount of current (Imax = EMF
rint )
16/21
PHYS 272 - David Blasing
Matter and Interactions: 20.1 - 20.7
Digital Multimeters
Non-Ideal Behaviors...
Batteries
Ohmic and non-ohmic
Batteries internal resistance
Model of a batteries internal resistance
A real battery is more accurately modeled by a constant EMF
source in parallel with an internal resistor (which typically is < 1Ω)
17/21
PHYS 272 - David Blasing
Matter and Interactions: 20.1 - 20.7
Digital Multimeters
Non-Ideal Behaviors...
Batteries
Ohmic and non-ohmic
Power
We previously used the result that the power (joules per second)
dissipated across a resistor was I 2 R. Let’s take that a step further.
18/21
PHYS 272 - David Blasing
Matter and Interactions: 20.1 - 20.7
Digital Multimeters
Non-Ideal Behaviors...
Batteries
Ohmic and non-ohmic
Power
We previously used the result that the power (joules per second)
dissipated across a resistor was I 2 R. Let’s take that a step further.
Change in electric potential energy, ∆U, required to change
the electric potential a charge q experiences is = q∆V
18/21
PHYS 272 - David Blasing
Matter and Interactions: 20.1 - 20.7
Digital Multimeters
Non-Ideal Behaviors...
Batteries
Ohmic and non-ohmic
Power
We previously used the result that the power (joules per second)
dissipated across a resistor was I 2 R. Let’s take that a step further.
Change in electric potential energy, ∆U, required to change
the electric potential a charge q experiences is = q∆V
If this is done in a time ∆t, then the power required to do
q∆V
this is ∆U
∆t = ∆t =
18/21
PHYS 272 - David Blasing
Matter and Interactions: 20.1 - 20.7
Digital Multimeters
Non-Ideal Behaviors...
Batteries
Ohmic and non-ohmic
Power
We previously used the result that the power (joules per second)
dissipated across a resistor was I 2 R. Let’s take that a step further.
Change in electric potential energy, ∆U, required to change
the electric potential a charge q experiences is = q∆V
If this is done in a time ∆t, then the power required to do
q∆V
this is ∆U
∆t = ∆t =I ∆V
18/21
PHYS 272 - David Blasing
Matter and Interactions: 20.1 - 20.7
Digital Multimeters
Non-Ideal Behaviors...
Batteries
Ohmic and non-ohmic
Power
We previously used the result that the power (joules per second)
dissipated across a resistor was I 2 R. Let’s take that a step further.
Change in electric potential energy, ∆U, required to change
the electric potential a charge q experiences is = q∆V
If this is done in a time ∆t, then the power required to do
q∆V
this is ∆U
∆t = ∆t =I ∆V
The electric power required to drive a current through a change in
electric potential
P = I ∆V
Notes:
1
Energy is conserved...so these joules per second are going
somewhere (often heat or light)
18/21
PHYS 272 - David Blasing
Matter and Interactions: 20.1 - 20.7
Digital Multimeters
Non-Ideal Behaviors...
Batteries
Ohmic and non-ohmic
Ohm’s law
1
|∆V | = EL for a conductive wire of length L
19/21
PHYS 272 - David Blasing
Matter and Interactions: 20.1 - 20.7
Digital Multimeters
Non-Ideal Behaviors...
Batteries
Ohmic and non-ohmic
Ohm’s law
1
|∆V | = EL for a conductive wire of length L
2
I
= ( µnA|q|
)L in the Drude model
19/21
PHYS 272 - David Blasing
Matter and Interactions: 20.1 - 20.7
Digital Multimeters
Non-Ideal Behaviors...
Batteries
Ohmic and non-ohmic
Ohm’s law
1
|∆V | = EL for a conductive wire of length L
2
I
= ( µnA|q|
)L in the Drude model
3
L
= I µnA|q|
19/21
PHYS 272 - David Blasing
Matter and Interactions: 20.1 - 20.7
Digital Multimeters
Non-Ideal Behaviors...
Batteries
Ohmic and non-ohmic
Ohm’s law
1
|∆V | = EL for a conductive wire of length L
2
I
= ( µnA|q|
)L in the Drude model
3
L
= I µnA|q|
4
L
= I σA
(Drude model assumes that I is independent of
conductivity σ)
19/21
PHYS 272 - David Blasing
Matter and Interactions: 20.1 - 20.7
Digital Multimeters
Non-Ideal Behaviors...
Batteries
Ohmic and non-ohmic
Ohm’s law
1
|∆V | = EL for a conductive wire of length L
2
I
= ( µnA|q|
)L in the Drude model
3
L
= I µnA|q|
4
5
L
= I σA
(Drude model assumes that I is independent of
conductivity σ)
I(R) where R is the resistance of the material
19/21
PHYS 272 - David Blasing
Matter and Interactions: 20.1 - 20.7
Digital Multimeters
Non-Ideal Behaviors...
Batteries
Ohmic and non-ohmic
Ohm’s law
1
|∆V | = EL for a conductive wire of length L
2
I
= ( µnA|q|
)L in the Drude model
3
L
= I µnA|q|
4
5
L
= I σA
(Drude model assumes that I is independent of
conductivity σ)
I(R) where R is the resistance of the material
Ohm’s Law
∆V = IR
Notes:
19/21
PHYS 272 - David Blasing
Matter and Interactions: 20.1 - 20.7
Digital Multimeters
Non-Ideal Behaviors...
Batteries
Ohmic and non-ohmic
Ohm’s law
1
|∆V | = EL for a conductive wire of length L
2
I
= ( µnA|q|
)L in the Drude model
3
L
= I µnA|q|
4
5
L
= I σA
(Drude model assumes that I is independent of
conductivity σ)
I(R) where R is the resistance of the material
Ohm’s Law
∆V = IR
Notes:
1
Ohm’s law only holds if resistance is not a function of I at all
2
Not true in an incandescent light bulb due to heat
19/21
PHYS 272 - David Blasing
Matter and Interactions: 20.1 - 20.7
Digital Multimeters
Non-Ideal Behaviors...
Batteries
Ohmic and non-ohmic
Ohmic vs non-ohmic devices examples
I linear with ∆V
(resistance is constant)
Resistance increases
n depends exponentially
with temperature, so less
on E, leading to
current at higher ∆V
“turn-on” voltage
20/21
PHYS 272 - David Blasing
Matter and Interactions: 20.1 - 20.7
Digital Multimeters
Non-Ideal Behaviors...
Batteries
Ohmic and non-ohmic
Brief review of this lecture
Model of a batteries internal resistance
A real battery is more accurately modeled by a constant EMF
source in parallel with an internal resistor (which typically is < 1Ω)
The electric power required to drive a current through a change in
electric potential
P = I ∆V
21/21
PHYS 272 - David Blasing
Matter and Interactions: 20.1 - 20.7