Resistance and Resistivity
• Resistance depends on the geometry of the
resistor – its length and cross-sectional area
– R is proportional to length
– R is inversely proportional to area.
rl
R
A
• Resistivity r depends on material properties
like how often charges scatter.
Power in a circuit
DE
P
Dt
• Power:
• In time Dt, a charge DQ enters on the left and
DQ exits on the right.
Vb
Va
Energy dissipated by a resistor
P  IV
V  IR
P  IV  I ( IR )  I 2 R
V2
V 
P  IV   V 
R
R
Four identical light bulbs are
connected to a power
supply as shown. Which
light bulb consumes the
most power?
1) B1
2) B2
3) B3
4) B4
B1
B2
B3
B4


V
5) They all consume the same amount of power.
Three identical light bulbs are connected in parallel
to a constant voltage power supply. Initially, switch
S1 is closed and the other two switches open. When
the other two switches, S2 and S3, are closed, the
brightness of the first light bulb
1) is dimmer.
s0
s1
s2
s3
2) is unchanged.
3) is brighter.
V


B1
B2
B3
Resistors in Series
Figure 26.31a
Resistors in Parallel
Figure 26.4a
Effective Resistance
1
1
1
 

• Parallel:
Reff R1 R2
R
• Series:
Reff  R1  R2 
rl
A
Effective Capacitance
• Parallel: Ceff  C1  C2  
C
• Series:
1
1
1



Ceff C1 C2
 0 A
d