Question

A length of wire has a resistance of 120 ohm. The wire is cut into N identical pieces that are then connected in parallel.
The resistance of the parallel arrangement is 1.875 ohm. Find N.​

Answer 1

Answer:

there is a direct equation for this that s the r effective is =total r/n^2

that is 120/.875=64 and its square root is 8 ..

that is n=8

Explanation:

Answer 2

The wire has been cut into 64 identical pieces.

When multiple resistors are connected in parallel, the overall resistance of the circuit is given by the reciprocal of the sum of the reciprocals of the individual resistances.

The formula is 1/R(total) = $1/R1 + 1/R2 + 1/R3 ... 1/Rn$

Where R(total) is the overall resistance of the parallel circuit, R1, R2, R3, ... Rn are the individual resistances.

Given that the resistance of the wire is 120 ohm and the resistance of the parallel arrangement is 1.875 ohm, we can use this formula to find N.

$1/R(total) = 1/120 + 1/R2 + 1/R3 + ... 1/Rn$

$1/1.875 = 1/120 + 1/R2 + 1/R3 + ... 1/Rn$

To find the value of N, we need to find out how many identical pieces the wire has been cut into.

So we can solve the above equation for n

$1/1.875 = 1/120 + n(1/R)$

$n(1/R) = 1/1.875 - 1/120$

$n = (1/1.875 - 1/120) * R$

n = 64

So the wire has been cut into 64 identical pieces.

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