Question

a wire of resistance 36ohm is cut into n equal parts and are joined in parallel. the Effective resistance is 1 ohm. the value of n is​

Answer 1

Concept:

Effective resistance: When two or more resistors are connected in a complex circuit, the effective resistance is the total resistance of all the resistors in the circuit.

Given:

A wire of resistance $36ohm$ is cut into $n$ parts and are joined in parallel.

Effective resistance, $R_{eq}=1ohm$

Find:

The value of $n$ .

Solution:

When a wire with resistance $R$ is cut into $n$ equal parts then the resistance of each part will be $\frac{R}{n}$ .

When these $n$ parts are joined in parallel, the equivalent or effective resistance will be:

$\frac{1}{R_{eq}} =\frac{1}{\frac{R}{n} } +\frac{1}{\frac{R}{n} } +\frac{1}{\frac{R}{n} } +\frac{1}{\frac{R}{n} } .....$

$R_{eq}=\frac{R}{n^2}$

Now,

The wire with resistance $=36ohm$

And $R_{eq}=1ohm$.

$R_{eq}=\frac{R}{n^2}$

$1=\frac{36}{n^2}$

$n^2=36\\n=6$

The value of $n$ is $6$ .

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Answer 2

Answer:

value of n is​ 6

Explanation:

Effective resistance: When two or more resistors are connected in a complex circuit, the effective resistance is the total resistance of all the resistors in the circuit.

Given:

A wire of resistance 36ohm  is cut into  parts and are joined in parallel.

Effective resistance, Req = 10 ohm

When a wire with resistance R is cut into  n equal parts then the resistance of each part will be R/n

When these  n parts are joined in parallel, the equivalent or effective resistance will be:

1/ Req =  1/ (R/N) + 1/ (R/N) + 1/ (R/N) +  ...............

Req  = R/n²

Now,

The wire with resistance = 36ohm

Req = 1 ohm

Req  = R/n²

1 = 36/ n²

n² = 36

n = 6

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