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)
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 .