Question

A potential difference of V=0.500 V is applied along a rectangular block of silicon (Si) with resistivity 8.70×10−4 Ω⋅m. The dimensions of the Si block are: width 1.50 mm; thickness 0.400 mm ; and length L=20.0 cm. You can assume that the current density in the Si block is uniform and that the currents in Si obey Ohm's law. What is the resistance of this Si block?

Answer 1

the resistance of the silicon block is 2.9 × 10^3 Ω

Step-by-step explanation:

The resistance (R) of a material can be calculated using the formula:

R = (ρ * L) / A

where ρ is the resistivity of the material, L is the length of the material, and A is the cross-sectional area of the material.

Given:

Resistivity of silicon (ρ) = 8.70 × 10^(-4) Ω⋅m

Length of the Si block (L) = 20.0 cm = 0.20 m

Width of the Si block = 1.50 mm = 0.0015 m

Thickness of the Si block = 0.400 mm = 0.0004 m

To find the cross-sectional area (A) of the Si block, we can multiply the width and thickness:

A = width * thickness = 0.0015 m * 0.0004 m = 6.0 × 10^(-7) m^2

Now, we can substitute the values into the resistance formula:

R = (ρ * L) / A

R = (8.70 × 10^(-4) Ω⋅m * 0.20 m) / (6.0 × 10^(-7) m^2)

R = 2.9 × 10^3 Ω