Two Great Minds Think Alike

Lately, I have learnt about two physicists that are considered noteworthy. The two people are Georg Simon Ohm and Gustav Robert Kirchhoff.

Ohm discovered that there was a proportional relationship between the voltage and the current that always calculated the same value for resistance (separate from other variables i.e temperature, calculation error). He came up with a general formula to represent the resistance and this was named the Ohm's Law.
 
Ohm's Law : R = V
                           --
                            I
where R is the resistance in volts/ ampere

Kirchhoff studied the way current and voltage was affected in series and parallel circuits respectively. He came up with two laws that we know as today:


Kirchhoff's Current Law: The total amount of current into a junction point of a circuit equals the total current that  flows out of the same junction

The current entering any junction is equal to the current leaving that junction. i₁ + i₄ = i₂ + i₃

        Kirchhoff's Voltage Law: The total of all electric potential decreases in any complete circuit loop is equal to any potential increases in that circuit loop. 

The sum of all the voltages around the loop is equal to zero. v₁ + v₂ + v₃ - v₄ = 0

Kirchoff's laws are improvements made on two other laws:

Conservation of Electric Charge: a law stating that the quantity of electric charge, the amount of positive charge minus the amount of negative charge in the universe, is always conserved

Conservation of Energy: a law stating that the total amount of energy in an isolated system remains constant over time, in other words conserved over time


Here are some important formulas to know to calculate current, voltage, or resistance in series circuits using the Ohm or Kirchhoff laws.

Resistance In Series:


From Kirchhoff's Law:     VT = V₁ + V₂ + V_{3  =} VN

                                                     IT = I₁  = I₂  = I_{3   =}   I_{N
 
From Ohm's Law :}     R_{T =} R₁ + R₂ + R_{3   =}  RN


_{In addition, if all the values of all the resistors in a series circuit are the same, the overall resistance can be determined by} 

R<sub>T = NR 
 where the total resistance is calculated by multiplying the total number of resistors (N) by the resistance of each individual resistor (R)

Resistances in Parallel: 

From Kirchhoff's Law:</sub>  I_{T  =}  I₁ + I₂ + I_{3  + IN}

                                                 V_{T =}  V₁  = V₂  = V<sub>3  = VN

From Ohm's Law :</sub>  1         1         1          1
                                      --   =   --    =   --    =   --  
                                     R_T         R₁      R₂        R₃ 

 In addition, if all the values of all the resistors in a parallel circuit are the same, the overall resistance can be determined by 
R_{T = R
         ---
         N
where the total resistance is calculated by divided the resistance of each individual resistor (R) by the total number of resistors (N)}