BASIC LAWS Ohm’s Law Kirchhoff’s Law Series resistors & voltage division Parallel resistors & current division Source Transformation Y -  transformation

Series resistors & voltage division Series: Two or more elements are in series if they are cascaded or connected sequentially and consequently carry the same current. The equivalent resistance of any number of resistors connected in a series is the sum of the individual resistances

Series resistors & voltage division Let’s say we want to find v 2 v 2 = iR 2 where, - Voltage Division Rule - Principle of Voltage Division Note that if R 2 >> R 1, then v 2  v

Series resistors & voltage division R1R1 R2R2 v i + v 1  + v 2 

Series resistors & voltage division R1R1 v R =  i= 0 + v 1  + v 2  If R 2 is replaced with open circuit, the resistance would be 

Parallel resistors & current division Parallel: Two or more elements are in parallel if they are connected to the same two nodes and consequently have the same voltage across them. The equivalent resistance of a circuit with N resistors in parallel is:

Parallel resistors & current division

Let’s say we want to find i 2 where, - Current Division Rule Parallel resistors & current division - Principle of Current Division +v+v +v+v

Parallel resistors & current division

Y  transformation Star  delta transformation How can we combine R 1 to R 7 ?

Delta -> StarStar -> Delta Y  transformation Star  delta transformation

Y  transformation Star  delta transformation example

Y  transformation Star  delta transformation example

Source transformation Another circuit simplifying technique It is the process of replacing a voltage source v S in series with a resistor R by a current source i S in parallel with a resistor R, or vice versa ++ R vsvs a b Terminal a-b sees: Open circuit voltage: v s Short circuit current: v s /R For this circuit to be equivalent, it must have the same terminal charateristics R isis a b

Source transformation Another circuit simplifying technique It is the process of replacing a voltage source vS in series with a resistor R by a current source iS in parallel with a resistor R, or vice versa Terminal a-b sees: Open circuit voltage: i s R Short circuit current: i s R isis a b

Source transformation Another circuit simplifying technique It is the process of replacing a voltage source vS in series with a resistor R by a current source iS in parallel with a resistor R, or vice versa Terminal a-b sees: Open circuit voltage: i s R Short circuit current: i s R isis a b ++ R vsvs a b Terminal a-b sees: Open circuit voltage: v s Short circuit current: v s /R

Source transformation Another circuit simplifying technique It is the process of replacing a voltage source vS in series with a resistor R by a current source iS in parallel with a resistor R, or vice versa ++ R vsvs a b For both to be equivalent, i s R = v s or i s = v s /R R isis a b

Source transformation Another circuit simplifying technique It is the process of replacing a voltage source vS in series with a resistor R by a current source iS in parallel with a resistor R, or vice versa ++ R vsvs a b R isis a b ixix iyiy Note: current through R (hence power) for both circuits is not the same i.e. i x  i y

Find v o in the circuit shown below using source transformation Example 1

Find i o in the circuit shown below using source transformation Example 2