Electric Notes

Fundamental Definition of Circuit Parameters

Voltage(V)

[dW/dq] Energy per unit charge created by seperation [W(J), q(c)]

Current (A)

[dq/dt(s)] The rate of charge flow [Deltaq=Integrali.dt]

Power (W)

[dW(J)/dt(s)] Energy per unit time (P=v.i) [DeltaW=IntegralP.dt]

Ideal Basic Circuit Element

If P>0 circuit absorbing power

If P<0 circuit delivering power

P=v.i

Ohm's Law

i=V/R

P=v.i=i^2.R=v^2/R

Power in resistive circuit

Wdissipated=IntegralP.dt

Wtotal dissipated=Integral(0 to infinity)P.dt

Kirchoff's Laws

Sum of the currents at a node is 0

KCL=Eİnode=0

Eİin=Eİout

Leaving current=+

Entering currents=-

Sum of the voltages around any closed path is 0

DeltaVloop=0

Method of using Kirchoff's Laws

2)Write KCL equations at nodes and KVL equations in loops as many as the number of unknowns

3)Solve n equations with n unknowns

1)Determine unknown currents

Be careful about the direction of currents and polarity of voltage

When there are dependent sources, express their values in terms of the unknowns in your equations

Resistive Circuits

Series Connection

Current is same

Req=ERi

Parallel Connection

Voltages are same

1/Req=E1/Req

Voltage Divider

Vj=Rj/Req.Vs

With only 2 resistors= Vi=Ri/(R1+R2).Vs

Current Divider

İj=(Req/Rj).İs

With only 2 resistors=İ1=R2/(R1+R2).İs

Delta-Y Equivalent Circuit

Delta-Y

Rx=(Neighbour sides)/(Sum of the Delta sides)

Y-Delta

Rx=(Sum of the multiplication of the Y sides)/(Pointing resistor)

Techniques of circuit analysis

1)Node-Voltage Method

Application of KCL

b)Pick a reference node (The node connects the most elements)

a)Determine essential node (Connects at least of 3 circuit elements)

c)Define node voltages (Voltage across essential nodes and reference node)

f)Solve linear equation set to obtain node-voltage (Classically or matrix evaluation)

d)write node-voltage equations (Sum of leaving cureents at essential nodes from KCL Eleaving=0)

e)Reorganize your equations in the form of AVnv=B)

If you have dependent source/s, define their value in terms of node-voltages so obtain "constraint equations"

If you have a voltage source (only voltage source either ind or dep) in terms of essential nodes. Use the technique of super node=Write a combined equation for both essential nodes)

2)Mesh-Current method

Application of KVL

1)Define mesh currents

2)Write mesh-current equations (sum of voltages around each meshes according to KVL DeltaVmesh=0)

4)Solve equation to obtain İmesh

3)Reorganize your equations as Aİmesh=B

If you have dependent sources, define their values in terms of mesh-current, so obtain "constraint equations"

If you have a only current source(Dep/Ind) between two meshes use supermesh, combine mesh equations

!! Watch out, do not define new currents, rather use predefined mesh-currents

Source Transformation

Thevenin and Norton Equivalents

Any resistive network containing ind. and dep. sources can be replaced by its Thevenin equivalent

Determination of Thevenin Equaivalent

General Method: Calculate open circuit voltage with request to intercoated terminals

Using source tranformation:(Finds Vth and Rth) but works with only independent sources

Deactivation Mode: (Find Rth)

Replace voltage sources with short cicuit

Replace current sources with open circuit

(Work only with independent sources)

Maximum Power Transfer

To obtain maximum power from a circuit on a load

RL=Rth

Pmax=Vth^2/4Rth

Superposition Technique

The response of a circuit can be obtained as the sum of responses from individual sources.

1)Pick a source and deactivate the others. Find solution 1.

2)Repeat for each sources

General Solution=Esolutioni

Inductive and Capacitive Circuits

Inductive

V=L(di/dt)

i=1/LINTEGRALVdt+i(0)

P=v.i=L.i.di/dt

Wstored=1/2Li^2

Winitial=1/2Li(0)^2

Wremaining=1/2[Li(t->0)]^2

Inductors behaves as short circuit when full

Capacitors

i=c(dV/dt)

V=1/cINTEGRALİdt+V(0)

P=v.i=c.V.(dV/dt)

Wstored=1/2cV^2

Winitial=1/2c(V(0))^2

Wremaining=1/2c(V(t->0))^2

Capacitors behaves as open circuit when full

Natural Response of RL circuits

İ(0^-)=İ(0^+)=I0

İ(t)=İ0e^-t/z

z=L/R

P=I^2Re^-2t/z

Wdissipated=1/2LIo^2(1-2e^-2t/z)

Wdiss=INTEGRAL(0->t)Pdt

Natural Response of RC circuits

V(0^-)=V(0^+)=V0

z=R.C

V(t)=V0e^-t/z

i(t)=(Vo/R)

e^-t/e

P=(V0^2/R)e^-2t/c

Wdiss=1/2CV0^2(1-e^-2t/c)