Consider a wire of length l, area of cross section A, and resistivity `rho` with resistance `10 Omega`. Its length is increased by applying a force, and it becomes four times of its original value. Find the changed resistance of the wire.

Consider a wire of length l, area of cross section A, and resistivity

1.	Consider a wire of length l, area of cross section A, and resistivity `rho` with resistance `10 Omega`. Its length is increased by applying a force, and it becomes four times of its original value. Find the changed resistance of the wire.
Answer» Here `I, A_1 = A, and R = 10 Omega` Similarly, `I_2 = 4I and R_2 = ?` Resistivity is same in each case as the meterail is same. The volume of the wire will remain the same even after the increase in the length. `A_1I_1 = A_2I_2 or A_2 = (A_1I_1)/(I_2) = (AI)/(4I) = (A)/(4)` The formula used for measuring resistacne of wire is `R = rho (I/A)` Using this formula in both cases, we have `R_1 = rho(I_1)/(A_1) =(rhoI)/(A) (i)` and `R_2 = rho(I_2)/(A_2) = rho(4I)/(A//4) = 16 rho(1)/(A)` (ii) Dividing Eq. (ii) by Eq. (i), `(R_2)/(R_1) = 16 or R, 160 Omega`

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Consider a wire of length l, area of cross section A, and resistivity `rho` with resistance `10 Omega`. Its length is increased by applying a force, and it becomes four times of its original value. Find the changed resistance of the wire.

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