A wire of resistance 10 ohm is stretched uniformly until its length becomes three times the original. What is its new resistance?

1. List the data: original $R = 10\,\Omega$, new length $= 3L$, same volume of wire. 2. Since volume is constant, if length becomes $3L$ then area becomes $A/3$. 3. Resistance formula is $R = \rho \dfrac{L}{A}$. 4. So $R' = \rho \dfrac{3L}{A/3} = 9\,\rho\dfrac{L}{A} = 9R$. 5. Hence $R' = 9 \times 10 = 90\,\Omega$. 6. Trap A (3.3) only divides by 3; trap B (30) multiplies length by 3 but ignores the area change; trap D (270) over-multiplies by an extra factor of 3. _Source: Samacheer Kalvi (TN SCERT) Class 10 Science, Unit 4 Electricity "Electricity", p.64_