Question

A piece of wire having a resistance of 5 ohm is cut into
5 equal parts. If the 5 parts of the
connected in parallel, find the effective
of the combination​

Answer 1

Considered a piece of wire having resistance 5 ohms, which is cut into 5 equal parts and is cut perpendicular to the length.

All five parts are connected in parallel.

We know that for Series resistance formula will be like Rs = R1 + R2 and for Parallel resistance formula will be like 1/Rp = 1/R1 + 1/R2

Now, given resistance is 5Ω and all are connected in parallel. Therefore, the resistance of the wire will be 5/R.

So,

1/Rp = 1/(R/5) + 1/(R/5) + 1/(R/5) + 1/(R/5) + 1/(R/5)

1/Rp = 5/R + 5/R + 5/R + 5/R + 5/R

1/Rp = (5 + 5 + 5 + 5 + 5)/R

1/Rp = 25/R

Rp= R/25 (Effective Resistance)

More Information

We know that,

R = p (l)/A

Here, The resistance of the conductor (wire) is directly proportional to the length of wire i.e. R ∝ l

Inversely proportional to the area of cross-section of wire i.e. R ∝ 1/A

R ∝ l/A

If we remove the sign of proportionality we use a constant i.e. p (rho).

Answer 2

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QUESTION :

A piece of wire having a resistance of 5 ohm is cut into 5 equal parts.

If the 5 parts of the connected in parallel, find the effective resistance of the combination.

SOLUTION :

From the given Question, we can obtain the following information......

A piece of wire having a resistance of 5 ohm is cut into 5 equal parts.

The 5 parts of the connected in parallel.

Let the original resistance of the be wire be R.

We know that the resistance in a conductor is directly Proportional to it's length.

So,

Now, the resistance in each of the five pieces of the wire is equal to R / 5.

Now, these are connected in parallel.

So,

In Parallel connection

1 / R equivalent = 1 / R_{1} + 1 / R _ { 2 } +........

So,

In this case here -

1 / R _ { Equivalent } = ( 5 / R ) × 5

=> 1 / R _ { Equivalent } = { 25 / R }

=> R equivalent = R / 25

So the net effective resistance of the combination is R / 25.

ANSWER :

THE net effective resistance of the combination is R / 25.