All About Resistors part-11

Circuit Analysis: 

The AC and DC behavior of resistors are the same. In series combination, the equivalent resistance is the sum of the resistances and is given by:

R = R1 + R2 + R3 +……

The current through the branch remains constant while voltage drops across different resistors are different and are given by the product of current and the individual resistances.                  

In shunt combination, the equivalent resistance is given by:

1/R = 1/R1 + 1/R2 +1/R3+…..

The voltage across branches remains constant while currents in different branches are different and are given by supply voltage divided by the individual resistances.

Through analysis, we can conclude that in case of two branch circuits, current in one branch is the product of supply current and the resistance in other branch divided by the sum of resistances. This is called ‘Shunt formulae’

I_R1 = I*R₂/ (R₁+R₂)

I_R2 = I*R₁/ (R₁+R₂)

There can also be star (Y and T) and delta (delta and pie) combination of resistances.

A delta network can be converted into star network by using the formulae:

R_A = R_AB*R_AC/ (R_AB+R_AC+R_BC)

R_B = R_AB*R_BC/ (R_AB+R_AC+R_BC)

R_C = R_AC*R_BC/ (R_AB+R_AC+R_BC)

Mnemonics - For delta to star conversion, the resistor at a node is the product of resistances in the adjacent branches connected to that node divided by the sum of all three delta resistances.

A star network can be converted into delta network by using the formulae:

R_AB = R_A +R_B +R_A*R_B/R_C 

R_{AC =} R_A +R_C +R_A*R_C/R_B

R_{BC =} R_C +R_B +R_C*R_B/R_A

Mnemonics - For star to delta conversion the resistance at a branch is the sum of the resistances held by the two nodes of the branch with the product of those resistances divided by the opposite resistance.