TOPIC :

Instantaneous power

Saad khan khattak shamsheer haider NaqviReg # 2120-fet/bsee/f13 reg # 2117-fet/bsee/f13

Contents

definition1

Mathematical representation2

Instantaneous power across resistor3

4

Instantaneous power across capacitor

Instantaneous power across inductor

5

4

6 Uses

Definition Instantaneous Power is the rate at

which energy is absorbed/delivered to an element at a specific time.

Instantaneous power varies with time.

Mathematical Representation

Mathematically instantaneous power is defined as product of function I(t) & v(t).

P(t)=I(t).V(t)

Where I(t)=Imcos(wt+θi) V(t)=Vmcos(wt+θv)

where Vm and Im are the amplitudes (or peak values), and θv and θi are the phase angles of the voltage and current

p(t) = v(t)i(t) = VmIm cos(ωt + θv) cos(ωt + θi)p(t) =1/2VmImcos(θv- θi)+1/2VmImcos(2wt+θv+ θi)

Instantaneous power across resistor

Voltage across resistor is defined by ohm law is

The instantaneous power delivered to the resistor is

Rtitv

R

tvRtitp2

2

Instantaneous power across inductor

Voltage across inductor is defined as:

The instantaneous power delivered to the inductor is

( )( ) di tv t Ldt

( ) dip t vi Lidt

Instantaneous power across capacitor

Current across capacitor is defined as: Ic(t)=Cdv/dt

The instantaneous power delivered to the capacitor is

( ) dvp t vi Cvdt

Uses of Instantaneous power We know that when we pay our bills to the electric

utility companies, we are paying for the electric energy consumed over a certain period of time.

Actually our bill is consummation of instantaneous power over certain period of time. Average power is average of instantaneous power

over one period and is mathematcally defined as t

p(t)=1/T∫P(t)dt 0

Starting of Automobile engine is example of instantaneous power.

Cracking is another example of instantaneous power.

Catapult is also example of instantaneous power.

Kick of donkey is also example of instantaneous power.

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