Question

A wire of given material having length l and area of cross section A has a resistance of 10 ohm what would be the resistance of another wire of the same material having length 1/4and area of cross section 2.5A

Answer 1

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Answer 2

Concept:

• The resistance of a wire
• The resistivity of a wire does not depend on the length and area of the cross section

Given:

• Length of wire = L
• Area of cross-section = A
• Resistance of wire = 10 ohm
• Length of new wire = L/4
• Area of cross section = 2.5A

Find:

• The new resistance of the wire

Solution:

Resistance = ρL/A

Resistance of original wire = 10ohm = ρL/A

Resistance of new wire = ρL/4A(2.5)

Resistance of new wire = ρL/10A = (1/10) ρL/A

But we know that ρL/A = 10 ohm

So, (1/10) ρL/A = 1/10 (10) = 1ohm

Resistance of new wire = 1 ohm

The new resistance of the wire is 1 ohm.

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