Ohm's Law

Current

• Current has units of (Columbs per Second), or (Amperes)

$$I=\frac{dQ}{dt}$$

• Current Density is the current per area

$$J=\frac{I}{A}$$

• Current measures the movement of coulombs through a wire, or a measured point on a wire.

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Charge Density

• Charge density is a property of a material
• It is based of of the amount of charges per unit m³
• n = Charge Density (Given constant, property of material)
• nq = Charge per m³
• If you multiply nq by speed V, it measures the charge passing through an area per unit time (Current Density)

$$J=vnq$$ $$\frac{I}{A}=vnq$$ $$V=\frac{I}{Anq}$$

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Resistivity

• Electrons move relatively slowly through a wire (still very fast, 2.3x10^-5 m/s for a copper wire)
• They do so because as charges move through the wire, they bump into molecules and elements of the wire itself.

$$\rho =\frac{E}{J}$$

• E = Electric Field
• J = Current Density
• ρ = Resistivity

Resistivity ρ is a property of the material itself. It is measured in units of (Volt meters/Amps)

Examples

• Copper: ρ = 1.68x10^-8 Vm/A (Not very resistive)
• Carbon: ρ = 5.00x10^-4 Vm/A (Some resistance)
• Wood: ρ = 10^-4 Vm/A (a lot of resistance)

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Resistance

Resistance (R), unlike Resistivity is a property of the object itself. It is measured in units of (Ohms)

• R has a unit of ohms

$$R=(\frac{L\rho }{A})$$ $$\Delta V=I(\frac{L\rho }{A})$$

and the big concept of resistance is

$$\Delta V=IR$$

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Power

Power (p) is the energy “lost” per unit time

$$P=\frac{dw}{dt}=\Delta V\frac{dq}{dt}$$ $$P=\Delta VI$$ $$P=I^{2}R$$ $$P=\Delta \frac{V^2}{R}$$

• Power has units of {J/S} (Joules per Second) or {W}
• 60 Watts would be equivalent to 60 Joules of energy being lost per second
• Resistance creates heat, and in extreme cases, light.
• This is a dissipation of energy
• This is a consequent of work.

Work

Work is required to move a charge As speed is constant, Kinetic Energy never changes.

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