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Asked in FBISE Physics 2023 — Paper 1 2023

Resistance of a wire is 'R' ohms. The wire is stretched to four times its length, then its resistance in ohms is

Correct answer: C. 16R

  • A. R/4
  • B. 4R
  • C. 16R
  • D. R/2

Explanation

The resistance of a wire is given by the formula: R=ρL /Awhere:R is the resistance,ρ is the resistivity of the material,L is the length of the wire, andA is the cross-sectional area of the wire.When the wire is stretched to four times its original length, the volume (and therefore the mass) of the wire remains constant. So, if the length is quadrupled, the cross-sectional area must be quartered.Let's denote the new resistance as R′, the new length as L′, and the new cross-sectional area as A′. We have: R′=ρL′ /A′Substituting L′=4L and A′=A/4 , we get: R′=ρ (4L)/(A/4) =16ρL/A =16RSo, the resistance of the wire will be 16 times the original resistance.

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About Resistance and Resistivity

Resistance measures opposition to current in a conductor and follows R = V/I for an ohmic conductor, while resistivity is an intrinsic property of the material. Questions use R = ρL/A, examine effects of length, cross-sectional area and temperature, and distinguish resistance, resistivity, conductance and conductivity.

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