Chapter 25

Electric CurrentsAnd Resistance

Physics for Scientists & Engineers, 3rd EditionDouglas C. Giancoli

© Prentice Hall

Figure 25-3

Figure 25-4 (a)

Figure 25-5

Figure 25-6

Figure 25-22

Figure 25-23

Figure 25-24

Figure 25-25

3P12-

Resistors & Ohm’s Law

RAρ

=

IRV =∆

parallel 1 2

1 1 1R R R

= +series 1 2R R R= +

Figure 25-7

Figure 26-2

P12-

Measuring Potential DifferenceA voltmeter must be hooked in parallel across the element you want to measure the potential difference across

Voltmeters have a very large resistance, so that they don’t affect the circuit too much

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Measuring CurrentAn ammeter must be hooked in series with the element you want to measure the current through

Ammeters have a very low resistance, so that they don’t affect the circuit too much

P12-

Measuring ResistanceAn ohmmeter must be hooked in parallel across the element you want to measure the resistance of

Here we are measuring R1

Ohmmeters apply a voltage and measure the current that flows. They typically won’t work if the resistor is powered (connected to a battery)

Figure 26-3 (a)

Figure 26-3 (b)

Figure 26-4 (a)

Figure 26-4 (b)

Figure 26-4 (a)

Figure 26-6

Figure 26-8

Figure 26-11

Figure 26-12

Figure 26-40

Figure 26-39

10P12-

(Dis)Charging a Capacitor1. When the direction of current flow is toward

the positive plate of a capacitor, then

dQIdt

= +

Charging

2. When the direction of current flow is away from the positive plate of a capacitor, then

DischargingdQIdt

= −

11P12-

Charging A Capacitor

What happens when we close switch S?

12P12-

Charging A Capacitor

NO CURRENTFLOWS!

0=−−=∆∑ IRCQV

ii ε

1. Arbitrarily assign direction of current2. Kirchhoff (walk in direction of current):

13P12-

Charging A CapacitorQ dQ RC dt

ε − =dQ dt

Q C RCε⇒ = −

−

0 0

Q tdQ dtQ C RCε = −−∫ ∫

A solution to this differential equation is:

( )/( ) 1 t RCQ t C eε −= −RC is the time constant, and has units of seconds

14P12-

Charging A Capacitor

/t RCdQI edt R

ε −= =( )/1 t RCQ C eε −= −

16P12-

Discharging A Capacitor

What happens when we close switch S?

17P12-

Discharging A Capacitor

NO CURRENTFLOWS!

dtdqI −=

0=−=∆∑ IRCqV

ii

18P12-

Discharging A Capacitor

0dq qdt RC

+ =0 0

Q t

Q

dq dtq RC

⇒ = −∫ ∫

/( ) t RCoQ t Q e−=

19P12-

General Comment: RCAll Quantities Either:

( )/FinalValue( ) Value 1 tt e τ−= − /

0Value( ) Value tt e τ−=

τ can be obtained from differential equation (prefactor on d/dt) e.g. τ = RC

20P12-

Exponential Decay

/0Value( ) Value tt e τ−=

Very common curve in physics/nature

How do you measure τ?

1) Fit curve (make sure you exclude data at both ends)

(t0,v0)

(t0+τ,v0/e)

2) a) Pick a pointb) Find point with y

value down by ec) Time difference is τ