Question

derive r¹+r²

this is 100 points question.​

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

Hello!

✍️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.

✍️ The potential difference V1, V2 and V3.

∴ V= V1+V2+V3 ...(1)

So, applying Ohm's law

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

 V1 = IR1                          

V2= IR2 and 

V3= IR3                    ... (3)

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

IR = IR1 + IR2 + IR3

IR = I ( R1 + R2 + R3 )

R = R1 + R2 + R3 ( Proved )

Thanks!❤