Elec1111 02a Power Energy
3
1 Electrical Engineering & Telecommunications Lecturer: Ted Spooner POWER & ENERGY Elec1111 Elec1111 Rm 124A EE email: [email protected] Power Power Power = time rate at which energy is consumed = time rate at which energy is consumed or produced or produced dw dw dq vi dt dq dt = ⋅ = ⋅ ⇒ Denoted by symbol Denoted by symbol p or or P Unit is watts, W Unit is watts, W p vi = ⋅ dt dw p = Energy t w pdτ −∞ = ⋅ ∫ Energy absorbed (passive convention): Energy absorbed (passive convention): Notation: Notation: w or or W Unit: joule, J Unit: joule, J ….. .. 1J = 1Watt second 1J = 1Watt second w p t Δ = Δ ⇒ w p t Δ = ⋅Δ If p is constant: • Energy supplied to or by element ? • Find +ve and –ve terminals • Convention: if +ve current enters +ve terminal then external source must expend energy to establish this current. (Passive Convention) v ab + - a b Terminal a is is positive with respect to terminal b. v ab + - a b Terminal a is v ab positive with respect to terminal b. i.e. Our Power Convention!!!!!!!!! • p=vi gives power absorbed by element • also called power dissipated by element • or power delivered to the element a b + v _ i Examples a b + v = 4 V _ i = 2 A Hence power absorbed is 8 W. p = vi = 8 W
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Transcript of Elec1111 02a Power Energy
1
Electrical Engineering & Telecommunications
Lecturer:Ted Spooner
POWER & ENERGY
Elec1111Elec1111
Rm 124A EE email: [email protected]
Power
PowerPower = time rate at which energy is consumed= time rate at which energy is consumedor producedor produced
dw dw dq v idt dq dt
= ⋅ = ⋅⇒
Denoted by symbol Denoted by symbol pp or or PPUnit is watts, WUnit is watts, W
p v i= ⋅dtdwp =
Energy
t
w p dτ−∞
= ⋅∫Energy absorbed (passive convention):Energy absorbed (passive convention):
Notation: Notation: ww or or WW
Unit: joule, J Unit: joule, J …….... 1J = 1Watt second1J = 1Watt second
wpt
Δ=Δ
⇒ w p tΔ = ⋅ΔIf p is constant:
• Energy supplied to or by element ?
• Find +ve and –ve terminals
• Convention: if +ve current enters +veterminal then external source must expend energy to establish this current. (Passive Convention)
vab+ -
a b Terminal a is
is positivewith respect to terminal b.vab
+ -a b Terminal a is
vab
positivewith respect to terminal b.i.e.
Our Power Convention!!!!!!!!!
• p=vi gives power absorbed by element• also called power dissipated by element• or power delivered to the element
a b
+ v _
i
Examples
a b+ v = 4 V
_
i = 2 A
Hencepower absorbed is 8 W.
p = vi = 8 W
2
Examples
a b+v = 5 V_
i = 2 A
Hence power absorbed is -10 W.
p = vi = -10 W
a b-v = -5 V+
i = 2 A
case (A): power absorbed by element is
case (B): power absorbed by element is
case (C): power absorbed by element is
case (D): power absorbed by element is
12W
+
12W
-12W
12W
Power & Energy Example• A radiator is connected to a power supply of
250V and draws a current of 4A.• P = V.I = 250 x 4• = 1000Watts = 1kW• If it is left on for 1 hour then the energy it
consumes is:
1kWhrrs Watthou100011000
.
===
= ∫x
dtpw
CIRCUIT ELEMENTS
Resistors
• Resistor = a circuit element that impedes flow of charge.
• Such a property is called resistance.
• Notation: R• Unit: ohm (Ω)
R
Power delivered to a resistor
vp vi vR
⎛ ⎞= = ⎜ ⎟⎝ ⎠
⇒2vp
R=
( )p vi iR i= = ⇒ 2p i R=
3
Resistors
coding using4 colour bands
Specifications:
1. value (Ω)2. tolerance (%)3. power dissipation (W)
thick-filmresistor<1mm
Power delivered to a resistor
240V100Ω1/4W
WRvp 576
10024022
=== Wp41
>
Parked car with lights left on for 4 hrs
12 26
vi AR
= = =
carbattery
R = 6Ω(lights)
i
_
+
v
12 2 24p vi W= = × =Power absorbed by R:
12sv V=
12sv v V= =
Energy = P . t
= 24 x 4 x 60 x 60 = 345600 J
= 96 Wh
