Question

5. The resistance of a wire varies directly with its length and inversely with
its area. If a certain piece of wire 10 m long and 0.10 cm in diameter has
a resistance of 100 ohms, what will its resistance be if its is uniformly
stretched so that its length becomes 12 m?
A. 80 B. 90 C. 144 D. 120​

Answer 1

Answer:

The resistance of a wire varies directly with its length and inversely with the square of its diameter. If 100 feet of wire with diameter 0.01 inch has a resistance of 80 ohms, what is the resistance of 90 feet of the same type of wire if its diameter is 0.04 inch?

Answer 2

Answer:

144 ohms

Step-by-step explanation:

Given: Length of wire = 10m

diameter of wire = 0.10 cm

Resistance = 100 ohms

New length = 12m

Concept : $R = k\frac{L}{A}$

                 where , k = Resistivity

                              R = Resistance

                               L = length

                               A = Area

Solution :

when the wire was stretched the dimensions were changed but the volume remained same, Let volum be V

then  $V = \frac{L}{A}$  ⇒ $A = \frac{V}{L}$                         ..........(1)

Using the above formula when R = 100 and L = 10,

$100 = k\frac{L}{A}$

using the value of A from equation (1)

⇒   $100 = k\frac{L}{\frac{V}{L} }$

here L = 10m then,

⇒ $100 = \frac{k}{V} * (10)^{2}$

⇒ K = 1           where, $K = \frac{k}{V}$

After Stretching L = 12

$R = k\frac{L}{A}$

⇒ $R = KL^{2}$

⇒ 1 × 12²

⇒ 144 ohms

∴ When the wire was stretched the resistance was increased to 144 ohms.

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