Electric Currents

Physics Department, New York City College of Technology

Key words Electric battery Electric current Resistance Ohm’s law Resistivity Electric energy Electric power Direct current

Alternating current

Average power rms values

Electric battery

A battery produces electricity by transforming chemical energy into electrical energy.

Electric battery

In a diagram of a circuit, it is denoted by the symbol

+

Electric current

Electric current is a flow of charge

Electric current

Current is defined as I is current ∆Q is the amount of charge that

passes through the conductor at any location

Δt is the time interval The unit of I is ampere (A)

t

QI

Direction of electric current

Electrical resistance

Defined as R is the resistance of a wire V is the potential difference applied

across the wire I is the current

The symbol of a resistor is

I

VR

Electron motion model

Disc 17, #22

Ohm’s law Resistance R is a

constant independent of V, i.e.,

Experimentally found by Ohm

Generally holds in metal conductors in room temperature

IRV

Ohm’s law

Disc 17, #19 Disc 17, #20 Disc 17, #21

Resistivity

It is experimentally found that

ρ is resistivity and depends on the material

L is the length of a wire A is the cross-sectional area

A

LR

Resistivity

Example #1 A flashlight bulb draws

300mA from its 1.5-V battery. (a) What is the resistance of the bulb?(b) If the battery becomes weak and voltage drops to 1.2V, how would the current change?

Example #1—continued

AmA 3.0300 (a)

0.53.0

5.1

A

V

I

VR

(b) mAAV

R

VI 24024.0

0.5

2.1

Example #2

Connect stereo to speakers. (a) If each wire must be 20m long, what diameter copper wire should be used to keep the resistance less than 0.10 Ω? (b) If the current is 4.0A, what is the potential difference across each wire?

Example #2—continued

(a)

268

104.310.0

)20)(1068.1(m

mm

R

LA

m 81068.1 iscopper for

.08.22

,04.11004.1, 32

mmrd

mmmA

rrA

(b) VAIRV 4.0)1.0)(0.4(

Electric energy Energy transformation between

electric and other forms are very common

Motors transform electric energy into mechanical energy

In electric heaters and hair dryers, electric energy is transformed into thermal energy

In a lightbulb, electric energy is transformed into light and thermal energy

Electric power The electric power transformed by any

device is P is electric power I is current V is potential difference

The unit of electric power is Watt (W) For a resistance R, we have

IVP

RIIRIIVP 2)(

R

VV

R

VIVP

2

)(

Example #3 Calculate the

resistance of a 40-W automobile headlight designed for 12V.

Example #3—continued

6.3)40(

)12(

12,4022

W

V

P

VR

VVWP

Alternating current The voltage and current produced by an

electric generator are sinusoidal

V0 is the peak voltage I0 is the peak current The frequency f is the number of complete

oscillations per second, and

tR

V

R

VI

tVftVV

sin

sin2sin

0

00

f 2

DC and AC

AC power

The power transformed in a resistance R at any instant is

The average power is calculated as

or

tRIRIP 220

2 sin

RIP 202

1

R

VP

20

2

1

AC power—continued

rms (root-mean-square) values rms values and

peak values

The average power in rms values:

VV

VV

II

II

rms

rms

707.02

707.02

02

002

R

V

R

VP

RIRIP

VIP

rms

rms

rmsrms

220

220

2

1

2

1

Example #4

(a) Calculate the resistance and the peak current in a 1000-W hair dryer connected to a 120-V line. (b) What if it is connected to a 240-V line in Britain?

Example #4

(a) AV

W

V

PI

rmsrms 33.8

120

1000

AII rms 8.1120

4.1433.8

120

A

V

I

VR

rms

rms

(b) WV

R

VP rms 4000

4.14

)240( 22