Question

A resistor of 5Ω is connected in series with a parallel combination of a number of resistors each of 5Ω. If the total resistance of the combination is 6Ω, how many resistors are in parallel?

Answer 1

1/Rp = (1/5) × x
Or, Rp=5/x ohm

Now,
5+5/x=6
Or, x=5

Hence, 5 resistors each of 5 ohm are connected in parallel combination.

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Answer 2

Answer:

5

Explanation:

Given, first a 5 Ω resistor is connected with parallel combination of number of resistor of 5 Ω. It is also given that total resistance of the combination is 6 Ω.

We know that, resultant of parallel combination for identical resistors is

$\boxed{R_p = \dfrac{R}{x}}$

Here, Rp = effective resultant in parallel

R = Identical resistance

x = number of identical resistance

Here, R = 5

So,

$\implies R_p = \dfrac{5}{x}$

Now, this Rp is in series with a 5 Ω resistance

We know that, if R₁ and R₂ are in series, then Rs series effective resistance is,

$\boxed{R_s = R_1 + R_2}$

So, here, R₁ = 5 Ω and R₂ = 5/x and Total resistance(Here Rs) = 6 Ω

Thus,

$\implies 6 = 5 + \dfrac{5}{x}$

$\implies 1 = \dfrac{5}{x}$

$\therefore \underline{\boxed{x = 5}}$

Thus, number of resistors in parallel are 5.

[Diagram of circuit is in the attachment. Please refer it. All the resistors of 5 Ω]

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