Question

Derive R = R1+ R2 + R3​

Answer 1

Answer:

Derivation:

Let there be three 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 flowing through all three resistances, So by applying Ohm's law three of them separately, 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

that is IR = I (R1+R2+R3)

R = R1+R2+R3

Hope it is helpful.