Question

Derive the expression for equivalent resistance in
series combinalion.

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Answer 1

Answer:

It is observed that the total current I, is equal to the sum of the separate currents through each branch of the combination.

I + I1 + I2 + I3

Let Rp be the equivalent resistance of the parallel combination of resistors. By applying Ohm's law to the parallel combination of resistors, we have  

I = V/Rp  

On applying Ohm's law to each resistor, we have  

I1 =   V/R1 ; I2 = V/R2; and I3 + V/R3    

From eqns. we have  

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

or 1/Rp =  1/R1 + 1/R2 +  1/R3

Thus, we may conclude that the reciprocal of the equivalent resistance of a group of resistances joined in parallel is equal to the sum of the reciprocals of the individuals resistances.

Explanation:

Answer 2

Answer:

In series combination, the total potential difference across the resistors is equal to the sum of individual resistances.

V=V₁+V₂+V₃      (1)

We know that from ohm's law,

V=IR

So, V₁=I₁R₁       (2)

V₂=I₂R₂            (3)

V₃=I₃R₃            (4)

Substituting (2), (3), (4) in (1)

We know that current remains constant in series connection

Hence, IR=I(R₁+R₂+R₃)

i.e., R=R₁+R₂+R₃

Explanation: