Question

If the resistance of a uniform wire of length $1,m$ of cross-sectional area $0.1,m^2$ is $12,\Omega$, then the resistance of wire of length $2,m$ of the same material with area of cross section $0.2,m^2$ is

• A. $24,\Omega$
• B. $6,\Omega$
• C. $12,\Omega$
• D. $40,\Omega$
• E. $4,\Omega$

Hint:

Physics Tip: If both length and area are doubled, $\frac{L}{A}$ remains same, so resistance remains unchanged.

Answer 1

The Correct Option is C

Concept:
Resistance of a wire is: $$R=\rho \frac{L}{A}$$ where $\rho$ = resistivity, $L$ = length, $A$ = area of cross-section.
Step 1: Use ratio method.
Same material means resistivity $\rho$ remains same. So, $$\frac{R_2}{R_1}=\frac{L_2/A_2}{L_1/A_1}$$ Given: $$R_1=12\Omega,\quad L_1=1,\quad A_1=0.1$$ $$L_2=2,\quad A_2=0.2$$
Step 2: Substitute values.
$$\frac{R_2}{12}=\frac{2/0.2}{1/0.1}$$ $$=\frac{10}{10}=1$$ So, $$R_2=12\Omega$$
Step 3: Final answer.
Hence required resistance is $12\Omega$. :contentReference[oaicite:0]{index=0}