A silicon crystal having a cross-sectional area of

Question

0.001 c m^{2}

and a length of

10^{- 3} c m

is connected at it's ends with 10v battery at temperature

300^{\circ} K

, when the current is 100mA. Find the resistivity and the conductivity?

Answer 1

Solution:
Given:

(A) a r e a = 0.001 c m^{2} (l) l e n g t h = 10^{- 3} c m V o l t a g e (V) = 10 v C u r r e n t = 100 m A = 100 \times 10^{- 3} A

We know that

R = \frac{V}{I} and R = \frac{ρ l}{A}

Where \rho=resistivity

\frac{V}{I} = \frac{ρ l}{A} ρ = \frac{V \cdot A}{I \cdot l} = \frac{(10) (0.001)}{(100 \times 10^{- 3}) (10^{- 3})} ρ = 100 Ω \cdot m

Conductivity (σ) = \frac{1}{ρ} = \frac{1}{100} = 0.01 (Ω \cdot m)^{- 2} σ = 0.01 (Ω \cdot m)^{- 1}

Answers (1)