Question

Find the resistance (in mega Ω) of a wire of length 8 m, cross sectional area 2 sq.cm and made of a material of resistivity 120 Ωm.
A) 1920 B) 4.8 C) 2.4 D) 960

Answer 1

Given that, a wire of length 8 m, cross sectional area 2 sq.cm and made of a material of resistivity 120 Ωm.

We have to find the resistance of the wire.

From above data we have; length (l) = 8 m, Area of cross-section (A) = 2 cm² and resistivity (p) = 120 Ωm.

We know that, Resistance of a wire is -

• directly proportional to length i.e.

R ∝ l

• inversely proportional to Area of cross-section i.e.

R ∝ 1/A

So,

R ∝ l/A

When we remove the sign of proportional then their comes a constant i.e. rho (p = resistivity)

R = p l/A

Now, substitute the known values in the above formula

Before that, convert area of cross-section into m².

1m = 100 cm

1m² = 10000 cm²

So,

Area of cross-section = 2 × 10⁴- m²

Now, substitute the values,

R = (120 × 8)/(2 × 10⁴-)

R = 60 × 8 × 10⁴

R = 480 × 10⁴

R = 4.8 × 10⁶ Ω

As said in question, we have to find the value of resistance in mega Ω.

So,

R = 4.8 mega Ω

Therefore, the value of resistance is 4.8 mega Ω.

Answer 2

Given ,

Length of a wire , l = 8 m

Area of cross section of wire , A = 2 cm²

⇒ Area , A = 2 * 10⁻⁴ m²

Resistivity of wire  , ρ = 120 Ωm

$\underbrace{\bold{R=\frac{\rho\; l}{A} }}$

where ,

• R denotes Resistance
• ρ denotes Resistivity
• l denotes length
• A denotes Area of cross-section

$\implies \bold{R=\frac{120*8}{2*10^{-4}} }\\\\\implies \bold{R=480*10^4}\\\\\implies \bold{R=4.8*10^6\; \Omega}\\\\\implies \bold{\bf{\blue{R=4.8\;M\Omega}}}$

So option (B) is correct.