Question

The equivalent resistance of 20 number of resistors of 20 ohm each
connected in parallel is-
(a) 10 ohm (b) 100 ohm (c) 1 ohm
(d) 20 ohm​

Answer 1

Given:-

→ Number of resistors = 20

→ Resistance of each resistor = 20 Ω

→ The resistors are connected in parallel.

To find:-

→ Equivalent resistance.

Solution:-

We know that, when n resistors are connected in parallel, their equivalent resistance Rₑ is given by :-

1/Rₑ = 1/R₁ + 1/R₂ + ... + 1/Rₙ

Substituting values in the above formula, we get :-

⇒ 1/Rₑ = 1/R₁ + 1/R₂ + ... + 1/R₂₀

⇒ 1/Rₑ = 1/20 + 1/20 + ... + 1/20

⇒ 1/Rₑ = 20/20

⇒ 1/Rₑ = 1

⇒ Rₑ = 1 Ω

Thus, equivalent resistance is 1 Ω [Option.(c)]

Some Extra Information:-

If resistors are connected in such a way that the same potential difference gets applied to each of them, they are said to be connected in parallel. The total current flowing into the combination is equal to the sum of the currents through the individual resistors.

Answer 2

Answer:

Given :-

• A resistance of 20 number of resistors of 20 ohm each connected in parallel.

To Find :-

• What is the equivalent resistance.

Solution :-

Given :

• Number of resistance = 20
• Resistors = 20 ohm

According to the question by using the formula we get,

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

$\implies \sf \dfrac{1}{R_e} =\: \dfrac{1}{R_1} + \dfrac{1}{R_2} + . . . . . + \dfrac{1}{R_{20}}$

$\implies \sf \dfrac{1}{R_e} =\: \dfrac{1}{20} + \dfrac{1}{20} + . . . . . + \dfrac{1}{20}$

$\implies \sf \dfrac{1}{R_e} =\: \dfrac{\cancel{20}}{\cancel{20}}$

$\implies \sf\bold{\red{\dfrac{1}{R_e} =\: 1\: \Omega}}$

$\therefore$ The equivalent resistance is 1 Ω .

Hence, the correct options is option no (c) 1 ohm or Ω .