Question

derive the formula of equivalent resistance of series combination of resistors​

Answer 1

Answer:

The same current flows through each resistor in series. Individual resistors in series do not get the total source voltage, but divide it. The total resistance in a series circuit is equal to the sum of the individual resistances: RN(series)=R1+R2+R3+… +RN.

Answer 2

GiveN :-

• Derive an equation for equivalent resistance of series combination of resistors with the help of diagram.

SolutioN :-

We need to derive the expression for equivalent resistance of a circuit when resistances are connected in series . So for that ,

Consider three resistors $\sf R_1 , \ R_2 \ \& \ R_3$ . Connect them I series as shown in the attachment . A battery of V volts has been connected to them and a current I is being drawn out of the cell . Let us take the potential differences across the three registers be $\sf V_1 , \ V_2 \ \& \ V _3$ respectively.

Sum of the potential difference across the three resistors should be equal to the applied voltage.

That is :-

$\sf:\implies \gray{ V = V_1 + V_2 + V_3}$

Let the effective resistance of the combination is R . And now the current flowing is I. So ,

★ According to the Ohm's Law :-

$\sf:\implies \pink{ V = I R }\\\\\sf:\implies V_1 + V_2+V_3= IR \\\\\sf:\implies IR_1+IR_2+IR_3=IR \\\\\sf:\implies I ( R_1+R_2+R_3)= IR \\\\\sf:\implies\underset{\blue{\sf Net \ Resistance \ in \ series}}{\underbrace{ \boxed{\pink{\frak{ R = R_1+R_2+R_3}}}}}$

Note :-

• For diagram refer to the attachment.