Question

Derive the relation between resistors R1,R2,R3 are connected in series in an electrical circuit?

Answer 1

Hey.

Here is the answer.

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Let there be 4 resistance R1, R2, R3 and R4 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, R3 is V3 and R4 is V4.

∴ V= V1+V2+V3+V4 ...(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=I R .....................(2)

∵ The same current is flowing through all four resistances, so by applying Ohm's law to four of them seperately, we will get 
 V1 = I R1                          
V2 = I R2
V3 = I R3  and            
V4 = I R4 ................................. (3)

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

I R = I R1 + I R2 + I R3 + I R4

i.e I R = I ( R1 + R2 + R3 + R4 )

⇒ R = R1 + R2 + R3 + R4

Derived.

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Thanks.