Question

The equivalent resistance of two resistors of equal resistances connected in parallel is _____ the value of each resistors.

options :-
a) half
b) twice
c) same
d) one fourth
please answer this correctly


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Answer 1

Explanation:

If the two resistances or impedances in parallel are equal and of the same value, then the total or equivalent resistance, RT is equal to half the value of one resistor. That is equal to R/2 and for three equal resistors in parallel, R/3, etc.

Answer 2

$\huge\mathfrak{Answer:}$

$\large\underline{\sf{\blue{Equivalent \: Resistance:}}}$

• The Equivalent resistance of two resistors of equal resistances connected in parallel is half the value of each resistors.
• Hence Option A is correct

$\large\underline{\sf{\blue{Proof:}}}$

Let us assume two identical resistor having resistance R are connected in parallel

Equivalent Resistance in parallel :

• If two resistance $\sf{R_1}$ and $\sf{R_1}$ are connected in parallel then their equivalent resistance is given by :

• $\boxed{\sf{\dfrac{1}{R_{eq}} = \dfrac{1}{R_1} + \dfrac{1}{R_2}}}$

$\large\underline{\mathfrak{\red{Equivalent \: resistance \: will \: be:}}}$

$\implies \sf{\dfrac{1}{R_{eq}} = \dfrac{1}{R} + \dfrac{1}{R}}$

$\implies \sf{\dfrac{1}{R_{eq}} = \dfrac{1 + 1}{R} }$

$\implies \sf{\dfrac{1}{R_{eq}} = \dfrac{2}{R} }$

Reciprocating Both sides of Equation

$\implies \boxed{\sf{R_{eq} = \dfrac{R}{2}}}$

If the two resistors in parallel are equal and of the same value

Then equivalent resistance is equal to half the value of one resistor.

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NOTE :

• If n number of identical resistor are connected in parallel then their equivalent resistance is given by R/n
• If n number of identical resistor are connected in series then their equivalent resistance is given by nR

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