Question

Three resistors of resistance Ra, R2 and Rs are connected as shown in figure. Equivalence
resistance is​

Answer 1

Given :

• Three resistors R₁ , R₂ and R₃ are connected as shown in figure

To Find :

• What will be equivalent resistance of the resistors

Solution :

By looking at the figure we come to know that, we have to connect R₂ and R₃ in parallel then their resultant will be connected with R₁ in series. Let's move ahead :

Arrange R₂ and R₃ in parallel and their resultant will be R₂₃ .

Formula for Parallel Combination is :

$\implies \sf{\dfrac{1}{R_p} \: = \: \dfrac{1}{R_1} \: + \: \dfrac{1}{R_2} \: + \: .... \: + \: \dfrac{1}{R_n}}$

Now, substituting values.

$\implies \sf{\dfrac{1}{R_{23}} \: = \: \dfrac{1}{R_2} \: + \: \dfrac{1}{R_3}} \\ \\ \implies \sf{\dfrac{1}{R_{23}} \: = \: \dfrac{R_2 \: + \: R_3}{R_2 R_3}} \\ \\ \implies \sf{R_{23} \: = \: \dfrac{R_2 R_3}{R_2 \: + \: R_3}}$

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Now, add the resultant of R₂ and R₃ with R₁ . So, Formula for series combination is :

$\implies \sf{R_s \: = \: R_1 \: + \: R_2 \: + \: .... \: + \: R_n}$

Substituting values

$\implies \sf{R_e \: = \: R_1 \: + \: R_{23}} \\ \\ \implies \sf{R_e \: = \: R_1 \: + \: \dfrac{R_2 R_3}{R_2 \: + \: R_3}} \\ \\ \implies \sf{R_e \: = \: \dfrac{(R_2 \: + \: R_3)R_1 \: + \: (R_2 R_3)}{R_2 \: + \: R_3}}$