Question

Driver a formula for equivalent resistance of three resistors R1 R2 R3 e are connected in parallel.​

Answer 1

GIVEN :-

• Equivalent resistance of 3 resistors R₁, R₂, R₃ are connected in Parallel.

TO DERIVE :-

• The formula for Equivalent resistance of 3 resistors R₁, R₂, R₃ are connected in Parallel.

DERIVATION :-

Accoding to Question , Three resistors are connected in parallel.

As We know that, In parallel connection pd across each resistor remains same.

Let current flow in R₁ be I₁ , R₂ be l₂ and R₃ be I₃

.

⇒ Net current flow in circuit = I

⇒ I = I₁ + I₂ + I₃

⇒ (V/R) = (V/R₁)+(V/R₂)+(V/R₃)

⇒ 1/R = 1/R₁ + 1/R₂ + 1/R₃

Note :- Refer to the attachment for required diagram.

Answer 2

Given :

• equivalent resistance of three resistors $R_1\:R_2\:R_3$ are connected in parallel.

To find :

• A formula for equivalent resistance of three resistors

According to the question :

↬An applied potential V produces current $I_1$ in $R_1$ , $I_2$ in $R_2$ , $I_3$ in $R_3$

↬Total current = $I = I_1 + I_2 + I_3$

Using Ohm's Law :

⟹ $I = \frac{V}{r}$

⟹ $I_1 = \frac{V}{r_1}$

⟹ $I_2 = \frac{V}{r_2}$

⟹ $I_3 = \frac{V}{r_3}$

↬If R is the equivalent resistance, then $I = \frac{V}{r}$

⟹ $\frac{V}{r} = ( \frac{V}{r_1} ) + ( \frac{V}{r_2} ) + ( \frac{V}{r_3} )$

We get :

⟹ $\frac{V}{r} = V [ ( \frac{V}{r_1} ) + ( \frac{V}{r_2} ) + ( \frac{V}{r_3} ) ]$

⟹ $\frac{V}{r} = ( \frac{1}{r_1} ) + ( \frac{1}{r_2} ) + ( \frac{1}{r_3} )$

So, It's Done !!