Question

A metal block has dimensions 10 cm x 5 cm x 2 cm. The ratio of maximum to minimum resistance
that can be obtained from i​

Answer 1

resistance of a wire is given as R = ρL/A

where ρ is specific resistance it depends on material.

so, resistance of wire is directly proportional to its length and inversely proportional to its cross sectional area.

i.e., R ∝ L/A

for minimum resistance,

taking L = 2cm, A = 10cm × 5cm

so, R(min) = ρ(2cm)/(10cm × 5cm).....(1)

for maximum resistance,

taking L = 10cm, A = 2cm × 5cm

so, R(max) = ρ(10cm)/(2cm × 5cm).....(2)

from equations (1) and (2),

R(max)/R(min) = (2cm)/(10cm) × (2cm × 5cm)/(10cm × 5cm)

= 1/5 × 1/(2 × 1)

= 1/10

hence, ratio of maximum and minimum resistance is 1 : 10

Answer 2

$\huge\bold\purple{Answer:-}$

resistance of a wire is given as R = ρL/A

where ρ is specific resistance it depends on material.

so, resistance of wire is directly proportional to its length and inversely proportional to its cross sectional area.

i.e., R ∝ L/A

for minimum resistance,

taking L = 2cm, A = 10cm × 5cm

so, R(min) = ρ(2cm)/(10cm × 5cm).....(1)

for maximum resistance,

taking L = 10cm, A = 2cm × 5cm

so, R(max) = ρ(10cm)/(2cm × 5cm).....(2)

from equations (1) and (2),

R(max)/R(min) = (2cm)/(10cm) × (2cm × 5cm)/(10cm × 5cm)

= 1/5 × 1/(2 × 1)

= 1/10

hence, ratio of maximum and minimum resistance is 1 : 10