Question

A piece of wire has a resistance of 0.45.
calculate the resistance of another wire of the same material with a third of the length and half the cross-sectional area. fig 8.1 shows a circuit with three resistors a power supply and four voltmeters

Answer 1

Answer:

0.34 ohm

Explanation:

Since the material of the wire is same, the resistivity doesn't change.

So let rho (resistivity) be constant for now. [Resistivity here is small r]

Now, 0.45 = r (L/A),

Then, 0.45 = r (L/3 / A/2)

Then, 0.45 = r (2L / 3A)

Then, 0.45 = r (2/3) (L/A)

So, 0.45 x 2/3 = r (L/A)       [ But r (L/A) = R ]

So, R = 45/ 100 X 2/3

= 15/50

= 3 / 10 ohm

= 0.34 ohm

Answer 2

$r = rho \times l \div a$

Original resistance = r

Original area of cross section = a

Original length = l

New resistance = R

New length (L) = 1/3 × l

New Area (A) = 1/2 × a

Resistivity (rho) remains same as the material of the wire is not changed.

Applying the formula

R = rho × (1/3 l) ÷ (1/2 a)

R = 2/3 (rho × l/a)

Substituting the value of rho × l/a

R = 2/3 r

r = 0.45 (Given)

R = 2/3 × 0.45

R = 2 × 0.15

R = 0.3

New resistance is 0.3 ohm.

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