ÎQ Ît ÎQ Ît
10 February
Current & Resistance Current is the flow of charge. Such a flow is produced by a potential difference. The current depends on the potential difference and the resistance. The resistance is a property of the material and the dimensions. A current dissipates energy in a resistor. This is the basis of many common devices. Circuit rules let us simplify complex circuits. We’ll look at series and parallel combinations.
Electric Fish The electric eel and the torpedo ray both use bioelectricity to stun and capture prey. The eel can produce a larger voltage, but the ray produces a larger current.
Black electrode at higher potential – negative reading Red electrode at higher potential – positive reading
Sources of Potential Work is done to raise charges in a battery to a higher potential. In the cell (another source of potential) this work is done by ion pumps. With emf, energy is replenished
Definition of current I=
ΔQ Δt
1 C/s = 1 amp = 1 A
The discharge of an electric eel can transfer a charge of 2.0 mC in a time of 2.0 ms. What current, in A, does this correspond to? I=
ΔQ Δt
−3
I=
2.0 x 10 C −3 2.0 x 10 sec
I = 1.0 A
How much is too much? Physiological effect
AC current (rms) (mA)
DC current (mA)
Threshold of sensation
1
3
Paralysis of respiratory muscles
15
60
Heart fibrillation, likely fatal
>100
>500
What determines the current? Adding a second battery increases the current. Changing wire dimensions – short thick wire → large current; long, thin wire → small current Changing wire material – a copper wire will carry a larger current than an iron wire of the same dimensions.
Our basic circuit I=
ΔV R Ohm’s law for a conductor of resistance R
Human Circuits Hand-to-hand resistance of a human with dry skin is quite variable, but we can assume a typical value of about 50 kΩ. If the “energy ball” produces a potential difference of about 1.5 V, what is the current through your body? Is this enough to feel? I=
ΔV R
I=
1.5 V 50 x 10 3 Ω
I = 30 μA
Determining resistance R=
ρL A Resistance of a wire in terms of resistivity and dimensions
How do they fit it in there? The filament of a 100 W bulb carries a current of 0.83 A at the normal operating voltage of 120 V. What is the resistance of the filament? I=
ΔV R
R=
ΔV I
R=
120V 0.83 A
R = 144 Ω If the filament is made of tungsten wire of diameter 0.035 mm, how long is the filament? R=
ρL A
L=
RA ρ
L=
( 144 Ω ) (π r 2) 5.0 x 10−7 Ωm
= .28 m = 28 cm
Energy and Power Pemf = Iε Power delivered by an emf
Chemical energy in the battery is transferred to potential energy of the charges in the current. The charges lose energy in collisions as they pass through the filament of the bulb. This energy is transformed to the thermal energy of the glowing filament.
Energy and Power in Resistors PR = IΔVR = I2R =
( Δ V R )2 R
Power dissipated by resistance R with current I and potential difference ΔVR Charges gain potential energy U in the battery. As charges accelerate in the electric field in the resistor, potential energy is transformed to kinetic energy K. Collisions with atoms in the resistor transform the kinetic energy of the charges to thermal energy Eth of the resistor.
Resistive Heating An electric blanket has a wire that runs through the interior. A current causes energy to be dissipated in the wire, warming the blanket. A new, low-voltage electric blanket is rated to be used at 18 V. It dissipates a power of 82 W. What is the resistance of the wire that runs through the blanket? 2
P=
( Δ V R) R
V ¿ R ¿¿ R= ¿ ¿ ¿ ¿ ¿ R=
(18 V )2 82W
R = 3.9 Ω
Current & Resistance Current is the flow of charge. Such a flow is produced by a potential difference. The current depends on the potential difference and the resistance. The resistance is a property of the material and the dimensions. A current dissipates energy in a resistor. This is the basis of many common devices. Circuit rules let us simplify complex circuits. We’ll look at series and parallel combinations.
Electric Fish The electric eel and the torpedo ray both use bioelectricity to stun and capture prey. The eel can produce a larger voltage, but the ray produces a larger current.
Black electrode at higher potential – negative reading Red electrode at higher potential – positive reading
Sources of Potential Work is done to raise charges in a battery to a higher potential. In the cell (another source of potential) this work is done by ion pumps. With emf, energy is replenished
Definition of current I=
ΔQ Δt
1 C/s = 1 amp = 1 A
The discharge of an electric eel can transfer a charge of 2.0 mC in a time of 2.0 ms. What current, in A, does this correspond to? I=
ΔQ Δt
−3
I=
2.0 x 10 C −3 2.0 x 10 sec
I = 1.0 A
How much is too much? Physiological effect
AC current (rms) (mA)
DC current (mA)
Threshold of sensation
1
3
Paralysis of respiratory muscles
15
60
Heart fibrillation, likely fatal
>100
>500
What determines the current? Adding a second battery increases the current. Changing wire dimensions – short thick wire → large current; long, thin wire → small current Changing wire material – a copper wire will carry a larger current than an iron wire of the same dimensions.
Our basic circuit I=
ΔV R Ohm’s law for a conductor of resistance R
Human Circuits Hand-to-hand resistance of a human with dry skin is quite variable, but we can assume a typical value of about 50 kΩ. If the “energy ball” produces a potential difference of about 1.5 V, what is the current through your body? Is this enough to feel? I=
ΔV R
I=
1.5 V 50 x 10 3 Ω
I = 30 μA
Determining resistance R=
ρL A Resistance of a wire in terms of resistivity and dimensions
How do they fit it in there? The filament of a 100 W bulb carries a current of 0.83 A at the normal operating voltage of 120 V. What is the resistance of the filament? I=
ΔV R
R=
ΔV I
R=
120V 0.83 A
R = 144 Ω If the filament is made of tungsten wire of diameter 0.035 mm, how long is the filament? R=
ρL A
L=
RA ρ
L=
( 144 Ω ) (π r 2) 5.0 x 10−7 Ωm
= .28 m = 28 cm
Energy and Power Pemf = Iε Power delivered by an emf
Chemical energy in the battery is transferred to potential energy of the charges in the current. The charges lose energy in collisions as they pass through the filament of the bulb. This energy is transformed to the thermal energy of the glowing filament.
Energy and Power in Resistors PR = IΔVR = I2R =
( Δ V R )2 R
Power dissipated by resistance R with current I and potential difference ΔVR Charges gain potential energy U in the battery. As charges accelerate in the electric field in the resistor, potential energy is transformed to kinetic energy K. Collisions with atoms in the resistor transform the kinetic energy of the charges to thermal energy Eth of the resistor.
Resistive Heating An electric blanket has a wire that runs through the interior. A current causes energy to be dissipated in the wire, warming the blanket. A new, low-voltage electric blanket is rated to be used at 18 V. It dissipates a power of 82 W. What is the resistance of the wire that runs through the blanket? 2
P=
( Δ V R) R
V ¿ R ¿¿ R= ¿ ¿ ¿ ¿ ¿ R=
(18 V )2 82W
R = 3.9 Ω
