160 Week 5: Resistance
- Adding resistors in parallel:
1
Rtot
=
1
R 1
+
1
R 2
+... (279)
- Kirchhoff’s Rules:
a)Loop Rule:The sum of the voltage changes around a circuitloopmust be zero (conser-
vation of energy).
b) Junction Rule:The sum of the currents flowing into a circuitjunctionmust be zero
(conservation of charge).- The battery described above is an “ideal” battery that can in principle deliver any amount of
power. Arealbattery (or other power supply) can never deliver an arbitrarily large electrical
power to a circuit. One model that (quite accurately) describes the limiting of power delivered
from a battery is that ofinternal resistance. In this model, a “real world” battery con-
sists oftwocomponents integrated inside the battery housing – a source of electrical energy
(usually chemical energy for traditional batteries) and an effectiveinternal resistanceof the
chemical medium and the rate limiting aspects of the chemistry itself.When power limitation
is important, batteries will usually be represented as:
+
+
−
−
Vint
internal resistance r
internal voltage
terminals (terminal voltage)
(where I have added a small representation of the terminals of a typical commercial battery
such as a D or AA cell).- When a real battery is deliveringnocurrent, the voltage drop across the internal resistance is
zero, and if the chemical “fuel” of the battery is not totally depleted, you will usually measure
an internal voltage determined by the chemical potential of the reaction itself. In this case,
the terminal voltage will be equal to the internal voltage, which is generally the nominal/rated
voltage of the battery or cell. When the cell is delivering currentI, however, the terminal
voltage (between the physical terminals on the ends of the battery) is:
Vterminal=Vint−Ir (280)The internal resistance determines themaximum current and power deliverable by the battery
when the battery isshort circuited– its terminals connected by a presumed perfect conductor.
They are:Imax=Vint
r(281)
and:
Pmax=VintImax=Vint^2
r