Question

If the length of a resistor is doubled and its cross-sectional area is decreased to half, then its resistance becomes:

Answer 1

Let,

• The length of resistor be L
• And area of cross section be A

Originally, the resistance will be;

• R = ρ L/A - - - - - - [equation i]

Now, following the condition as mentioned in question;

• Length = 2L
• Area = A/2

So, the new resistance will be;

• R' = ρ 2L/ A/2
• R' = ρ 2L × 2 /A
• R' = ρ 4L/A
• R' = 4 p L/A - - - - - - [ from equation i, we can write p L/A = R ]
• R' = 4R

Therefore, the resistance becomes 4 times the original resistance.

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