A cylindrical conductor of length 2 m and area of cross-section 0.2 ~mm ² carries an electric current of 1.6 A when its ends are connected to a 2 V battery. Mobility of electrons in the conductor is 10⁻³ ~m ² / V. s . The value of is : (electron concentration =5 10²⁸ / m ³ and electron charge .=1.6 10⁻¹⁹ C )

Step-by-step solution

For a cylindrical conductor with length 2 m, cross-section 0.2 mm² = 0.2 × 10⁻⁶ m², carrying 1.6 A at 2 V. Resistance: R = V/I = 2/1.6 = 1.25 Ω. Resistivity: = RA/L = 1.25 0.2 10⁻⁶/2 = 0.125 10⁻⁶ Ω·m. Using = 1/(ne ) , mobility: = 1/(ne ) = 1/(5 10²⁸ 1.6 10⁻¹⁹ 0.125 10⁻⁶) = 1/(1 10^3) = 10⁻³ m²/V·s. Thus = 1 .