Chapter 26
Current, Resistance &
Ohm’s Law
Potential difference and charge flow
Battery produces potential difference causing flow
of charge in conductor
Current:
I = dq/dt
dq is charge that passes the surface in time dt
Units: C/s = ampere = A
• Drift velocity: average net velocity of electrons
~ mm/s
• Signal velocity: speed of electric field
= speed of light in the material ~108 m/s
V
I
Device
• Ohm’s law: for some devices (conductors), I is
proportional to V:
I
V = IR
V
• R = Resistance = proportionality constant = V/I
I
V
• Current depends on voltage
I
I
Device
and on the device
I
V
V
V
• Resistance R = V / I, not necessarily constant
V
I
Device
• Ohmic material obeys Ohm’s Law: R is constant
• R is a property of the device
• images:
surface mount
Resistivity
• Property of material; zero for superconductors
• For cylindrical conductor:
A
• R is proportional to L
• R is proportional to 1/A
L
• R is proportional to L / A
• Define resistivity ρ as the proportionality constant
L
R=ρ
A
Temperature dependence
• Resistivity is approx, linear with temperature:
Define
ρ = a + bT
ρ0 = resistivity at T = T0
ρ0 = a + bT0 → a = ρ0 − bT0
ρ = ρ0 + b(T − T 0 )
ρ / ρ0 = 1+ α(T − T 0 )
α = coefficient of resistivity (C º )
-1
ρ = ρ0 (1+ α(T − T 0 )) ⇒ R = R0 (1+ α(T − T 0 ))
For metals, α > 0 (resistance increases with temp)
For semiconductors, α < 0 (resistance decreases)