Week 5: Resistance
- Abattery is a chemical device that functions as a “persistent capacitor” that can deliver
charge at a given voltage for a very long time. In a sense, it is made upof a vast number
of tiny molecular-scale capacitors in parallel, each one of which is “neutralized” as charge is
transferred. Batteries store and deliver energy as they function as a source of electriccurrent.
The symbol for a battery (or other persistent voltagesource) in an electric circuit is:
V
+
Technically, this symbol is for an electricalcell, and a battery is a collection of cells in series
(with their voltages adding to create a higher voltage than we could otherwise create with the
chemical process) but the terms will be used interchangeably in thisintroductory work.
- Current is defined as:
I=
∆Q
∆t
=
dQ
dt
(273)
This is the charge per unit time flowing (for example) from one terminal of a battery to the
other or from one plate of a capacitor to the other through a conducting pathway.
- Ohm’s Law is:
∆V=IR (274)
which can be modelled from:
R=ρL
A
= L
σA
(275)
whereLis the length of the material,Ais its cross-sectional area,ρ= 1/σis itsresistivity
whereσis itsconductivity. Since ∆V=EL(the potential difference across it is the uniform
field inside times the length) we can also write Ohm’s Law as:
J~=∆Q
A∆t
nˆ=σE~ (276)
whereJ~is the vectorcurrent density. From this we can see thatelectric fields are not zero in
a conductor carrying a current!
- The power dissipated by a resistance carrying a current is:
P=V I=V
2
R
=I^2 R (277)
where the first form is the easiest to understand.
- Adding resistors in series:
Rtot=R 1 +R 2 +... (278)
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