resistance of a system of resistors

 

             RESISTANCE OF A SYSTEM OF RESISTORS

 

 

THERE ARE MAINLY TWO METHODS OF JOINING THE RESISTORS  OR COMBINATION OF RESISTORS.

ONE IS SERIES COMBINATION AND OTHERS IS PARALLEL COMBINATION.

 

RESISTORS IN SERIES :--

IN A ELECTRIC CIRCUIT , RESISTORS HAVING RESISTANCE R1,R2,R3 ….. Rn RESPECTIVELY  ARE CONNECTED TO EACH OTHER END TOE END POINTS. THEN THE RESISTORS ARE SAID TO BE CONNECTED IN SERIES.

 

 

 

 

 

 

HERE THREE RESISTORS  R1 ,R2 , R3 ARE CONNECTED TO ENDS X AND Y OF THE SERIES COMBINATIONS.

IN THE RESISTORS IN SERIES OR COMBINATION OF SERIES , THE VALUE OF THE CURRENT IS THE SAME AND ITS POSITION IS INDEPENDENT IN THE ENTIRE ELECTRIC CIRCUIT.

IT MEANS TO SAY THAT THE CURRENT IN EVERY PART OF THE CIRCUIT WILL BE SAME IN SERIES COMBINATION AND SAME CURRENT FLOWS THROUGH EACH AND EVERY RESISTANCE.

HERE, THE POTENTIAL DIFFERENCE (PD) OF EACH RESISTORS IS VARY. SO POTENTIAL DIFFERENCE ACROSS COMBINATION OF RESISTORS IN SERIES IS EQUAL TO THE SUM OF POTENTIAL DIFFERENCE ACROSS THE INDIVIDUAL RESISTORS.

IT MEANS:--

V = V1 + V2 + V3

 

 

 

NOW , IN THE GIVEN CIRCUIT , LET US CONSIDERS THAT CURRENT FLOWING THROUGH THE CIRCUIT IS I . SO , THE ELCTRIC CURRENT PASSING THROUGH EACH RESISTORS IS I.

 

NOW , ALL RESISTORS CONNECTED IN SERIES COMBINATION CAN BE REPLACED BY AN EQUVALENT SINGLE RESISTOR OF RESISTANCE R , SO THAT POTENTIAL DIFFERENCE (V) AND CURRENT FLOWING THROUGH THE CIRCUIT REMAINS SAME.

APPLYING OHMS LAW TO THE ELECTRIC CIRCUIT, WE HAVE

V = IR

 

NOW ON APPLYING OHMS LAW TO THE ALL THREE RESISTORS SEPARATELY

V = I R1

V = IR2

V = IR3

 

NOW PUT THE VALUES OF V1, V2 , V3 IN EQUATION (1)

IR = IR1 + IR2 + IR3

R = R1+R2+R3

 

 

 

 

(2) RESISTORS IN PARALLEL:--

IN AN ELECTRIC CIRCUIT , RESISTORS HAVING RESISTANCE R1 , R2 , R3…..Rn  RESPECTIVELY ARE CONNECTED TO EACH OTHER BETWEEN ENDS POINTS. THEN RESISTORS ARE SAID TO RESISTORS IN PARALLEL.

 

 

 

 

 

 

 

IN THE RESISTORS   R1    ,  R2 , R3 IN PARALLEL OR COMBINATION OF PARALLEL , POTENTIAL DIFFERENCE IS SAME.  

 THEN , TOTAL CURRENT I IS EQUAL TO THE SUM OF THE SEPARATE CURRENTS PASSING THROUGH EACH RESISTANCE CONNECTED IN PARALLEL COMBINATION.

 

I = I1+I2+I3

LET AND THE EQUIVALENT RESISTANCE OF THE PARALLEL COMBINATION IS   Rp. ON APPLYING OHMS LAW TO THE PARALLEL COMBINATIONS OF THE RESISTORS. WE GET

 

I = V / Rp

 

ON APPLYING OHMS LAW TO EACH RESISTORS CONNECTED IN PARALLEL  COMBINATIONS, WE GET

I1 = V / R1

I2 = V / R2

I = V/ R3

FROM THE ABOVE EQUATIONS , WE GET

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

1/Rp = 1/R1+1/R2+1/R3

HENCE,  WE GET RESULTS THAT THE RECIPROCAL OF THE EQUIVALENT RESISTANCE OF THE PARALLEL COMBINATION IS EQUAL TO THE SUM OF THE RECIPROCALOF THE INDIVIDUALS RESISTANCES.