egr 1301 electrical work egr 1301: introduction to engineering

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EGR 1301 Electrical Work EGR 1301: Introduction to Engineering

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Page 1: EGR 1301 Electrical Work EGR 1301: Introduction to Engineering

EGR 1301

Electrical Work

EGR 1301: Introduction to Engineering

Page 2: EGR 1301 Electrical Work EGR 1301: Introduction to Engineering

EGR 1301

Electrical WorkMethod 1

• Work (or Energy) = Force x Distance Force = magnetic force on electrons Distance = traveled in wire or resistor

Vbatt RI

Vdrop = IR

+

-

+

-

Page 3: EGR 1301 Electrical Work EGR 1301: Introduction to Engineering

EGR 1301

Voltage – What Is It?

• Energy per unit charge of current

• 1 Volt =

• Or V = E/Q• So E = VQ

1 Coulomb (charge)

1 Joule (energy)

Page 4: EGR 1301 Electrical Work EGR 1301: Introduction to Engineering

EGR 1301

Example 1:Battery

• A charge of Q = 50 C flows through a 12 V battery. a) How much energy is imparted to the

charge? E = VQ = (12 V)(50 C) = 240 J b) Where does the energy come from? The electro-chemical reactions in the

battery.

Page 5: EGR 1301 Electrical Work EGR 1301: Introduction to Engineering

EGR 1301

Electrical WorkMethod 2

• Recall: Power = Energy/Time So, or

• Recall: Power = Voltage*Current (P =VI) So,

Vbatt RI

Vdrop = IR

+

-

+

-

tE

P = E = Pt

RV2

E = VIt = t = I2Rt

Page 6: EGR 1301 Electrical Work EGR 1301: Introduction to Engineering

EGR 1301

Example 2:Water Heater

• How much energy does a hot water heater use if it draws 10 A from a 120 V wall outlet for 1 hour? I = 10 A, V = 120 V, t = 1 hr = 3600 s E = VIt = (120 V)(10 A)(3600 s) = 4.32 MJ Units check:

• V*A*s = J/C * C/s * s = J

Page 7: EGR 1301 Electrical Work EGR 1301: Introduction to Engineering

EGR 1301

Capacitors

• Energy is stored in electric field between the plates.

• Recall:• From method 1: E = QV

V C

+

-

VQ

C =

++ ++

- - - -

Conductor

Insulator

Stored Charge

or Q = VC

Page 8: EGR 1301 Electrical Work EGR 1301: Introduction to Engineering

EGR 1301

Capacitors

• From previous slide: E = QV and Q = VC• Charge builds up on either side of

capacitor

• Each bit of charge requires more energy

V C

+

-

++ ++

- - - -VVV

VQE QdVdE

VVEVCdVQdVdE

000

2

2

1CVE

Page 9: EGR 1301 Electrical Work EGR 1301: Introduction to Engineering

EGR 1301

Example 3:Capacitor

• A 50 μF capacitor is charged to 10 V. What energy is stored? C = 50 μF, V = 10 V E = ½CV2 = ½(50 μF)(10 V)2

= ½(50x10-6 F)(10 V)2 = 2.5x10-3 J = 2.5 mJ

Page 10: EGR 1301 Electrical Work EGR 1301: Introduction to Engineering

EGR 1301

Example 3:Camera Flash

• Assume a light bulb and a camera flash give the same light per unit energy.

• The camera flash has a 100 μF capacitor, charged to 250 V.

• How many 60 W light bulbs is this energy usage equivalent to if the camera discharges in t = 0.01 s?

Page 11: EGR 1301 Electrical Work EGR 1301: Introduction to Engineering

EGR 1301

Example 3:Camera Flash

• How many 60W light bulbs is this energy usage equivalent to if the camera discharges in t = 0.01 s? C = 100 μF, V = 250 V, t = 0.01 s E = ½CV2 = ½(100x10-6 F)(250 V)2 = 3.125 J 1 bulb: E = Pt Ebulbs = NPt = N(60 W)(0.01 s) = 0.6*N J

0.6*N J = 3.125 J N = 3.125/0.6 = 5.21 bulbs

Page 12: EGR 1301 Electrical Work EGR 1301: Introduction to Engineering

EGR 1301

Inductor

• Energy is stored in magnetic field inside the coil.

• Similar to the capacitor, except using current instead of voltage

2

2

1LIE

L

+ -V

I