Question

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

Answer 1

Answer:

Explanation:

The diagram of three resistors connected in series combination is shown.

R  1R  

2

​  

 and R  

3

​  

 are the three resistors.

I = electric current flowing through the circuit

V = the potential difference supplied by the battery

Applying the Ohm’s law to the entire circuit, we have

V=IR

On applying Ohm’s law to the three resistors separately, we further have

V  

1

​  

=IR  

1

​  

 

V  

2

​  

=IR  

2

​  

 

and V  

3

​  

=IR  

3

​  

 

The total potential difference across a combination of resistors in series is equal to the sum of potential difference across the individual resistors. That is,

V=V  

1

​  

+V  

2

​  

+V  

3

​  

 

Therefore, IR=IR  

1

​  

+IR  

2

​  

+IR  

3

​  

 

or

Equivalent resistance of the combination, R=R  

1

​  

+R  

2

​  

+R  

3

​

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.