A wire of copper having length I and area of cross-section A is taken and a current I is flown through it. The power dissipated in the wire is P. If we take an aluminium wire having same dimensions and pass the same current through it, the power dissipate

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Q: 39 (CDS-I/2018)
A wire of copper having length I and area of cross-section A is taken and a current I is flown through it. The power dissipated in the wire is P. If we take an aluminium wire having same dimensions and pass the same current through it, the power dissipated will be

question_subject: 

Geography

question_exam: 

CDS-I

stats: 

0,6,7,2,3,6,2

keywords: 

{'aluminium wire': [0, 0, 0, 1], 'copper': [1, 0, 1, 1], 'wire': [0, 0, 7, 16], 'power': [24, 3, 21, 61], 'same current': [0, 0, 0, 2]}

The power dissipated in a wire can be calculated using the formula P = I^2 * R, where P is the power dissipated, I is the current flowing through the wire, and R is the resistance of the wire.

In this scenario, the length (L) and area of cross-section (A) of the copper wire are given. Since the resistance of a wire is proportional to its length and inversely proportional to its cross-sectional area, the resistance of the copper wire can be calculated as R_copper = ρ_copper * (L / A), where ρ_copper is the resistivity of copper.

Now, if we replace the copper wire with an aluminum wire having the same dimensions (length and cross-sectional area), the resistance can be calculated as R_aluminum = ρ_aluminum * (L / A), where ρ_aluminum is the resistivity of aluminum.

Since the resistivity of aluminum is higher than that of copper, the aluminum wire will have a higher resistance. Therefore, when the same current I flows through the aluminum wire, the power dissipated can be calculated as P_aluminum = I^2 * R_aluminum.

Comparing the power dissipated in the two wires, P_copper and P_al