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**Current**I ≡ dq / dt

is measured in**Amperes**(1 A ≡ 1 C / s).Its direction is conventionally the direction of movement positive charge carriers would have, from positive to negative potential, even though the charge carriers are actually negative. So electrons move in the opposite direction to the current!

Viewed as charges "drifting" down a wire, I = ρ v_{drift}A, where A is the cross-sectional area of the wire.- We define the
**current density**J ≡ I / A. For many materials of interest,J = σ E = E / ρ

where here σ is the**conductivity**of the conductor and ρ is now the**resistivity**. Note that**E**is no longer zero inside the conductor: it is the cause of the current. Assuming a uniform electric field, we haveJ = ΔV / (ρ l)

and**Ohm's law**:ΔV = I (ρ l / A)

where R is measured in Ω (≡ I R

**Ohms**). - The resistivity is a function of temperature; expanding in a Taylor series, and truncating after the linear term, we have
ρ(T) = ρ

where α is the_{0}+ dρ/dT (T_{0}) * (T - T_{0})≡ ρ

_{0}(1 + α (T - T_{0}))**temperature coefficient of resistivity**. - A
**resistor**dissipates electrical power at the rate ofP = dU/dt

= d(q ΔV)/dt

= I ΔV.

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©2010, Kenneth R. Koehler. All Rights Reserved. This document may be freely reproduced provided that this copyright notice is included.

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