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BASIC LAWS • Ohm’s Law • Kirchhoff’s Law • Series resistors & voltage division • Parallel resistors & current division • Y - transformation • Source 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 N Req R1 R2 R N Rn n 1 Series resistors & voltage division Let’s say we want to find v2 v2 = iR2 R2 v2 v R 1 R 2 where, i v R 1 R 2 - Voltage Division Rule - Principle of Voltage Division Note that if R2 >> R1, then v2 v Series resistors & voltage division i R1 + v1 v R2 + v2 Series resistors & voltage division i=0 v R1 R = + v1 + v2 If R2 is replaced with open circuit, the resistance would be R2 v2 v v2 v R1 R2 R1 v1 v v1 0 R1 R2 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: 1 1 1 1 Req R1 R2 RN Parallel resistors & current division Parallel resistors & current division + + v v v i2 R2 R1 i2 i R1 R2 Let’s say we want to find i2 where, v iR eq R1R2 i R1 R2 - Current Division Rule - Principle of Current Division Parallel resistors & current division i2 R1 i i2 i R1 R2 i1 R2 i i1 0 R1 R2 i2 R1 i i2 0 R1 R2 i1 R2 i i1 i R1 R2 Y Star transformation delta transformation How can we combine R1 to R7 ? Y Star transformation delta transformation Delta -> Star Star -> Delta Rb Rc R1 ( Ra Rb Rc ) Ra R1 R2 R2 R3 R3 R1 R1 Rc Ra R2 ( Ra Rb Rc ) Rb R1 R2 R2 R3 R3 R1 R2 Ra Rb R3 ( Ra Rb Rc ) Rc R1 R2 R2 R3 R3 R1 R3 Y transformation Star example delta transformation Y transformation Star example delta transformation 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 a a is vs + R b Terminal a-b sees: Open circuit voltage: vs Short circuit current: vs/R b For this circuit to be equivalent, it must have the same terminal charateristics 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 a is R b Terminal a-b sees: Open circuit voltage: isR Short circuit current: is 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 a is a R vs + b Terminal a-b sees: Open circuit voltage: isR Short circuit current: is b Terminal a-b sees: Open circuit voltage: vs Short circuit current: vs/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 a is a R vs + b For both to be equivalent, b isR = vs or is = vs/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 a is a iy R vs + ix b b Note: current through R (hence power) for both circuits is not the same i.e. ix iy Example 1 Find vo in the circuit shown below using source transformation Example 1 Example 2 Find io in the circuit shown below using source transformation