Question

N identical resistors each of resistance R are
connected in parallel. The equivalent resistance
of the combination will be:​

Answer 1

Given

n identical resistors each of resistance R are  connected in parallel

To Find

Equivalent resistance

Solution

If n resistors are connected in parallel ,

$\bf \pink{\bigstar\ \; \dfrac{1}{R_{eq}}=\dfrac{1}{R_1}+\dfrac{1}{R_2}+\dfrac{1}{R_3}+...}$

If all are identical ,

i.e., R₁ = R₂ = R₃ = ... = R ( say )

$\implies \rm \dfrac{1}{R_{eq}}=\dfrac{1}{R}+\dfrac{1}{R}+\dfrac{1}{R}+...\\\\\implies \rm \dfrac{1}{R_{eq}}=\dfrac{n}{R}\\\\\implies \bf \green{R_{eq}=\dfrac{R}{n}\ \; \bigstar}$

Answer 2

Given :-

• N identical resistors each of resistance R are connected in parallel.

To Find :-

• Equivalent Resistance Of the Combination.

Solution :-

If they are parallel then,

1/R_eq = 1/R¹ + 1/R² + 1/R³.....

If we say that they are identical then,

Let, R¹ = R² = R³ = R.

So,

➨ 1/R_eq = 1/R + 1/R + 1/R....

➨ 1/R_eq = n/R.

➨ R_eq = R/n.

✔ Hence, Your Answer is R/n.