Resistance and Resistivity Resistance depends on the geometry of the - - PowerPoint PPT Presentation

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.

• Resistivity r depends on material properties

like how often charges scatter.

l R A r 

Power in a circuit

• Power:
• In time Dt, a charge DQ enters on the left and

DQ exits on the right.

E P t D  D

Vb Va

Energy dissipated by a resistor

P IV V IR  

2

( ) P IV I IR I R   

2

V V P IV V R R         

B2 B3 B4 V   B1

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 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. 2) is unchanged. 3) is brighter.

V   s0 s1 s2 s3 B1 B2 B3

Figure 26.31a

Resistors in Series

Figure 26.4a

Resistors in Parallel

Effective Resistance

• Parallel:
• Series:

1 2 eff

R R R   

1 2

1 1 1

eff

R R R    l R A r 

Effective Capacitance

• Parallel:
• Series:

1 2 eff

C C C   

1 2

1 1 1

eff

C C C   

0A

C d  