Tutorials

Simplifying circuits

- One of the best and easy way to determine the unknown value in a circuit is to simplify the circuit. In this tutorial, I will introduce valid ways of how to combine resistors and transform elements in a circuit to create a one loop circuit. 

Resistors (series and parallel)

                                                                       Series
                                                           Req= R1+ R2 + R3

- Resistors in series can simply be added.

                                                                      Parallel
                                                       1/Rt= 1/R1+ 1/R2+ 1/R3
                                                                   Rt= R123

-Resistors in parallel can be combined by using the product over sum rule or by using the formula above.



Capacitor (series and parallel)

                                                                      Series
                                                      1/Ct= 1/C1+ 1/C2+ 1/C3
                                                                   Ct= C123

- Capacitors follow the same law in using the reciprocals. The total capacitance of capacitors in series is equal to the reciprocal of the sum of the reciprocals of their individual capacitances.

                                                                  Parallel
                                                          Ct= C1+ C2+ C3

- Capacitors in parallel can simply be added.

Wye - Delta / Delta - Wye

- In this process, I will transform three resistors in triangle form into a Y form and in Y form into triangle form. This process will help to simplify resistor combination.

How to transform Delta - Wye?

R1= Ra(Rb)/ Ra+Rb+Rc

R2= Rb(Rc)/ Ra+Rb+Rc

R3= Ra(Rc)/ Ra+Rb+Rc

- The formula for this process is resistor 1(2 or 3) equal to the product of the two resistors at the side of resistor 1(2 or 3) divided by the sum of all the three resistors.

How to transform Wye - Delta?

                                                   Ra= R2(R3)+ R3(R1)+ R1(R2)/ R2
                                                   Rb= R2(R3)+ R3(R1)+ R1(R2)/ R3
                                                   Rc= R2(R3)+ R3(R1)+ R1(R2)/ R1
- The formula for this process is resistor a(b or c) equal to the sum of the product of the three resistors 1, 2, and 3 divided by the resistor away from resistor a(b or c).  


Example problems for this tutorial will be shown soon...