A metal cube with sides of length a has electrical resistance r between opposite faces
Answers
Answer:
Resistance R is given by :-
R = ρl/A
Where ρ is resistivity ; l is the length parallel to which current flows and A is the area through which the current flows.
In this case,
R = ρl/(l^2) = ρ/l (taking side of cube as l)
dividing the cube into 27 smaller cubes, We know the fact that volume of the cubes finally is equal to the initial volume of the cube.(basically mass conservation, but cancelling density on both sides)
l^3 = 27a^3 (a is the side of one small cube)
a = l/3
Therefore resistance across two opposite faces of a small cube :-
r = ρ(a)/a^2 = ρ/a = 3ρ/l = 3R
therefore new resistance is 3 times the original resistance.
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Answer:
R = ρl/A
Where ρ is resistivity ; l is the length parallel to which current flows and A is the area through which the current flows.
In this case,
R = ρl/(l^2) = ρ/l (taking side of cube as l)
dividing the cube into 27 smaller cubes, We know the fact that volume of the cubes finally is equal to the initial volume of the cube.(basically mass conservation, but cancelling density on both sides)
l^3 = 27a^3 (a is the side of one small cube)
a = l/3
Therefore resistance across two opposite faces of a small cube :-
r = ρ(a)/a^2 = ρ/a = 3ρ/l = 3R
therefore new resistance is 3 times the original resistance.