Combination of resistances

Combination of resistances

In this topic we will discuss about combination of resistances , i.e series and parallel combination of resistances .

Combination of resistances –

Series combination In series combination resistors are connected end to end with one another . resistors are said to be connected in series , when same current passes through the resistors  when potential difference applied across the connected  resistors .

Let , three resistors  of resistance R1, R2,and R3 are connected in series with external source E as shown in figure (a) . Let  I be the current flowing through the each resistors , their respective potential differences are V1, V2 and  V3 .

According to Ohm’s law  here,  V1 = I R1  ,    V2 = I R2   ,  and   V3 = I R3

Let, RS is the equivalent resistance of the combination as shown in figure (b) ,

then , V = I RS

But net potential V = V1+ V2 +V3

Then  IRS  = I R1 + I R2 + I R3

So ,  RS  =  R1 +  R2 +  R3  ……………………This the equation of equivalent resistance .

 Parallel combination –  Two or more resistors are said to be in parallel if potential difference across each resistors are same but currents are different . In parallel combination one end of each resistors are connected at one point and other ends at another point .

Let three resistors of resistance R1 , R2 and R3 are connected in parallel as shown in figure (a) with external source . let V be the potential difference of the end A and B . I1, I2 and  I3 are the currents flowing through the resistors .

 

According to Ohm’s law  I=V/R .

SO, I1=V/R1 , I2=V/R2 and I3=V/R3

Let, Rp is the equivalent resistance of the combination as shown in figure (b)

Then I=V/Rp

But I = I1+ I2 + I3

V/Rp = V/R1 + V/R2 + V/R3

SO, 1/Rp = 1/R1 + 1/R2 + 1/R3 …………………….. equation for equivalent resistance .

 

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