Question

Derive the relation R= R1+R2+R3 when three resistors R1,R2,R3 are connected in series in an electrical circuit?

Answer 1

Derivation:
Let there be 3 resistance R1, R2, and R3 connected in series. A battery of V volts has been applied to the ends of this series combination. Now suppose the potential difference across the resistance R1 is V1, R2 is V2 and R3 is V3.

∴ V= V1+V2+V3 ...(1)

Now, suppose the total resistance of the combination be R, and the current flowing through the whole circuit be I.
So, applying Ohm's law to the whole circuit, we get :

V/I = R or V=IR ...(2)

∵ The same current is flowing through all three resistances, so by applying Ohm's law to three of them seperately, we will get 
 V1 = IR1                          
V2= IR2 and 
V3= IR3                    ... (3)

 Now, putting (3) and (2) in equation (1), we get

IR = IR1 + IR2 + IR3
i.e IR = I ( R1 + R2 + R3 )
⇒ R = R1 + R2 + R3 

Hence its derived

Answer 2

Answer:

hello

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Derivation:

Let there be 3 resistance R1, R2, and R3 connected in series. A battery of V volts has been applied to the ends of this series combination. Now suppose the potential difference across the resistance R1 is V1, R2 is V2 and R3 is V3.

∴ V= V1+V2+V3 ...(1)

Now, suppose the total resistance of the combination be R, and the current flowing through the whole circuit be I.

So, applying Ohm's law to the whole circuit, we get :

V/I = R or V=IR ...(2)

∵ The same current is flowing through all three resistances, so by applying Ohm's law to three of them seperately, we will get  

V1 = IR1                          

V2= IR2 and  

V3= IR3                    ... (3)

Now, putting (3) and (2) in equation (1), we get

IR = IR1 + IR2 + IR3

i.e IR = I ( R1 + R2 + R3 )

⇒ R = R1 + R2 + R3  

Hence its derived

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