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Two wires of same material have length L and 2L and cross-sectional areas 4A and A respectively. The ratio of their specific resistance would be
- a)1 : 2
- b)8 : 1
- c)1 : 8
- d)1 : 1
Correct answer is option 'D'. Can you explain this answer?
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Most Upvoted Answer
Two wires of same material have length L and 2L and cross-sectional ar...
Explanation:
- Specific resistance (ρ) is given by the formula: ρ = R * A / L
- Where R is the resistance, A is the cross-sectional area, and L is the length of the wire
Given:
- Wire 1: Length L, Area 4A
- Wire 2: Length 2L, Area A
Let's find the specific resistance for each wire:
- For wire 1:
ρ1 = R1 * 4A / L
- For wire 2:
ρ2 = R2 * A / 2L
Ratio of specific resistance:
- Ratio of specific resistance = ρ1 / ρ2
- Substitute the values of ρ1 and ρ2:
( R1 * 4A / L ) / ( R2 * A / 2L )
= 4R1 / R2
Given:
The material of both wires is the same, so resistivity (ρ) is the same for both wires.
Resistances of the wires are given by:
- R1 = ρ * L / 4A
- R2 = ρ * 2L / A
Substitute R1 and R2 in the ratio equation:
= 4( ρ * L / 4A ) / ( ρ * 2L / A )
= ( ρ * L ) / ( ρ * 2L )
= 1
Therefore, the ratio of specific resistance of the two wires is 1:1. Hence, the correct answer is option 'D'.
- Specific resistance (ρ) is given by the formula: ρ = R * A / L
- Where R is the resistance, A is the cross-sectional area, and L is the length of the wire
Given:
- Wire 1: Length L, Area 4A
- Wire 2: Length 2L, Area A
Let's find the specific resistance for each wire:
- For wire 1:
ρ1 = R1 * 4A / L
- For wire 2:
ρ2 = R2 * A / 2L
Ratio of specific resistance:
- Ratio of specific resistance = ρ1 / ρ2
- Substitute the values of ρ1 and ρ2:
( R1 * 4A / L ) / ( R2 * A / 2L )
= 4R1 / R2
Given:
The material of both wires is the same, so resistivity (ρ) is the same for both wires.
Resistances of the wires are given by:
- R1 = ρ * L / 4A
- R2 = ρ * 2L / A
Substitute R1 and R2 in the ratio equation:
= 4( ρ * L / 4A ) / ( ρ * 2L / A )
= ( ρ * L ) / ( ρ * 2L )
= 1
Therefore, the ratio of specific resistance of the two wires is 1:1. Hence, the correct answer is option 'D'.
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Two wires of same material have length L and 2L and cross-sectional areas 4A and A respectively. The ratio of their specific resistance would bea)1 : 2b)8 : 1c)1 : 8d)1 : 1Correct answer is option 'D'. Can you explain this answer?
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