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In the 1st case,
Length = l
Area = a
R = (rho*l) by a
In the 2nd case,
Length' = l' = l by 2
Area' = a' = 2a
R' = (Rho * l') by a'
= [Rho * (l by2)] by 2a
= (Rho * l) by 4a
= [(Rho * l) by a] * 1/4
= R * 1/4
R' by R = 1 by 4
The new resistance is 1 fourth of the old resistance
Length = l
Area = a
R = (rho*l) by a
In the 2nd case,
Length' = l' = l by 2
Area' = a' = 2a
R' = (Rho * l') by a'
= [Rho * (l by2)] by 2a
= (Rho * l) by 4a
= [(Rho * l) by a] * 1/4
= R * 1/4
R' by R = 1 by 4
The new resistance is 1 fourth of the old resistance
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