JEE Main · 2024 · 04 Apr 2024 · Shift 2 · Current Electricity

Two wires A and B are made up of the same material and have the same mass. Wire A has radius of 2.0 mm and wire

B

has radius of 4.0 mm. The resistance of wire B is

2Ω

. The resistance of wire A is ____

Ω

Answer: 32

Solution

Same material and same mass

\Rightarrow

same volume:

π r^{2} L = constant \Rightarrow L \propto \frac{1}{r ^{2}}

.
Resistance:

R = \frac{ρ L}{π r ^{2}} \propto \frac{1}{r ^{2}} \cdot \frac{1}{r ^{2}} = \frac{1}{r ^{4}}

\frac{R _{A}}{R _{B}} = (\frac{r _{B}}{r _{A}})^{4} = (\frac{4}{2})^{4} = 16

R_{A} = 16 \times R_{B} = 16 \times 2 = 32 Ω

JEE Main · 2024 · 04 Apr 2024 · Shift 2 · Integer answer