Question

Its urgent pls pls pls
Qno 1

Answer 1

Answer:

2 metre.

Explanation:

Let the lengths of the two sections be $\mathrm{l_1 \: and \: l_2}$.

Since the resistance is $1 \Omega /m$, the respective resistances of the sections are $\mathrm{ l_1 \: and \: l_2.}$

By using the formula for resistances in parallel, we have the equivalent resistance as:

$R_{eq}=1.8 \Omega =\frac{ l_1 \cdot l_2}{l_1+l_2}\\</p><p>1.8= \frac {l_1 \cdot l_2}{20}\\</p><p>\text {But the total length is 20m}\\</p><p>1.8 \times 20= l_1 (l_1-20)\\</p><p>\implies l_1^2-20l_1-36=0\\</p><p>(l_1-18)(l_1-2)=0\\</p><p>\text{Since we want the length of smaller part, 2 is the answer}$

Answer 2

Answer:

2m

Explanation:

According to the given question,

Total resistance = 20 ohm

Equivalent resistance = 1.8 ohm

We are asked to find length of shorter section.

Let,

Resistance of shorter section = R1

Resistance of bigger section = R2

According to the question,

• R1+R2 = 20 -------1)

• 1/R1 + 1/R2 = 1/1.8 -----2)

So, by equation 2)

• R1×R2/R1+R2 = 1.8

• R1R2/20 = 1.8

(By equation 1)

• R1R2 = 36 ohm

• R1 = 36/R2

Putting this value in equation 1)

• 36/R2 +R2 = 20

Let R2 = x

Then, 36/x + x = 20

• 36+x^2 = 20x

• x^2-20x+36 =0

• (x-18)(x-2) = 0

Since R1 is shorter in length hence,

• R2 = 18 ohm

• R1 = 2 ohm

Again, Resistance is 1ohm/ m

Thus, Length of short part is 2m ans.