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Current and Resistance

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  1. Current and Resistance Chapter 27

  2. Electric Current • Flow of electric charges through a piece of material • Amount of flow depends on material and the potential difference across the material • Whenever there is a net flow of charge through a region= there is an electric current

  3. Electric Current • Current (I): the rate at which charge flows through a surface • Unit of current is ampere= A • If ΔQ is the amount of charge that passes though the surface in time (Δt) the average current Iavg= ΔQ/ΔI • Electric Current I= dQ/dt • 1A= 1C/s

  4. Electric Current • The direction of the current is opposite the direction of the flow of electrons • Refer to a moving charge as charge carrier • If the ends of a conducting wire are connected the electric field is zero within the conductor • No net transport of charge • Also no current

  5. Resistance • Current density (J) units of ampere/meter2 • J=I/A • I= nqVdA then J= nqVd • This above equation is ONLY VALID if current density is UNIFORM and only if the cross-sectional area A is PERPENDICULAR to the direction of the current

  6. Resistance • Ohm’s Law • For many materials, the ratio of the current density to the electric field is a constant σ that is independent of the electric field producing the current • J=σE • Further derivations show that R=L/σA which is called resistance

  7. Resistance • Resistance (R) unit is ohm (Ω) • R= ΔV/I • 1Ω= 1V/A • circuits use elements called resistors to control the current in the circuit at different places: • Two types are: • Composition resistor • Wire-wound resistor

  8. Resistance • Resistivity is the inverse of conductivity • ρ=1/σ • Unity is Ohm meters (Ωm) • Resistance of a uniform material of length(L) • R= ρ x L/A • If the length of wire is doubled, its resistance doubles • If its area is doubled, its resistance decreases by ½

  9. Resistance and Temperature • Variation of Resistance with temperature • ρ=po[1+α(T-To)] • ρ=resistivity at some temp. T (°C) • α is the temperature coefficient of resistivity • Temperature Coefficient of Resistivity • α= (1/ρo)x(Δρ/ΔT) • Δρ= ρ - ρo

  10. Superconductors • Class of metals and compounds whose resistance decreases to zero when they are below a certain temp. (Tc)

  11. Electrical Power • Power (P) is the rate at which energy is delivered to the resistor by a battery • P= IΔV • Unit= Watt • Power delivered by voltage source to any device • P=I2R = (ΔV)2/R • Unit of power= Watt