Question

resistance.
3. Explain the parallel combination of resistors and derive the formula of equivalent
​

Answer 1

Answer: In series combination, resister are connected end to end and current has a single path through the circuit but the potential difference varies across each resistor. Thus we can write as,

V = V1 + V2 + V3

according to Ohm's law V = IR So,

V1 = I R1, V2 = I R2, V3 = I R3

V = I R1 + I R2 + I R3

V = I(R1+R2+R3)

V =IRe

All the individual resistances become equal to the equivalent resistance.

or Re = R1 + R2 + R3......Rn

In parallel combination, each resistor is connected to the positive terminal while the other end is connected to a negative terminal. The potential difference across each resistance is the same and the current passing through them is different.

V = V1 =V2=V3

I = I1+ I2+I3

Current throught each resistor will be:

I1= V/R1 , I2 = V/R2 = I3 = V/R3

I = V (1/R1+ 1/R2+1/R3)

In case of equivalent resistance I=V/Re

V/Re = V (1/R1+ 1/R2+1/R3)

So the equivalnet resistance is the sum of all resistances

1/Re = 1/R1+ 1/R2+1/R3

Explanation:

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.