36.2k views
2 votes
A metallic rod has a length 1.5m and a diameter 0.2 cm. The rod carries a current of 5A

when a p.d of 75V is applied between its ends.

(a) Find the current density in the rod.

(b) Calculate the magnitude of the electric field applied to the rod.

(c) Calculate the resistivity and conductivity of the material of the rod.​

User Lizzy
by
5.5k points

2 Answers

4 votes

Final answer:

The current density in the rod is 1.59 x 10^6 A/m^2. The magnitude of the electric field applied to the rod is 75V. The resistivity of the material is 4.72 × 10^-5 Ω·m and the conductivity is 2.12 × 10^4 Ω^ -1 ·m^ -1.

Step-by-step explanation:

To find the current density, we first need to calculate the cross-sectional area of the rod. The formula for the area of a circle is A = πr^2, where r is the radius of the circle. In this case, the diameter of the rod is given as 0.2 cm, so the radius is 0.1 cm or 0.001 m. Therefore, the area is A = π(0.001^2) = 3.14 x 10^-6 m^2.

Current density (J) is defined as the current (I) divided by the cross-sectional area (A). So, J = I/A = 5A / 3.14 x 10^-6 m^2 = 1.59 x 10^6 A/m^2. Therefore, the current density in the rod is 1.59 x 10^6 A/m^2.

To calculate the magnitude of the electric field (E), we can use Ohm's Law. Ohm's Law states that the electric field (E) is equal to the current density (J) multiplied by the resistivity (ρ).

The formula for Ohm's Law is E = J × ρ. Rearranging the formula, we can solve for ρ: ρ = E / J = 75V / 1.59 × 10^6 A/m^2 = 4.72 × 10^-5 Ω·m.

The resistivity (ρ) of a material is the reciprocal of its conductivity (σ). So, the conductivity of the material can be calculated as σ = 1/ρ = 1 / 4.72 × 10^-5 Ω·m = 2.12 × 10^4 Ω^ -1 ·m^ -1.

User Bidisha
by
5.7k points
2 votes

Answer:

Step-by-step explanation:

Current density J = i / A where i is current and A is cross sectional area

J = 5 / π x ( .1 x 10⁻² )²

= 1.6 x 10⁶ A / m²

b )

electric field applied E = V / l where V is potential difference and l is lemgth of rod

E = 75 / 1.5

= 50 v / m

c )

J = σ E

J is current density , σ is conductivity and E is electric field .

1.6 x 10⁶ = σ x 50

σ = 3.2 x 10⁴ Ω⁻¹ m⁻¹

Resistivity = 1 / σ

= 1 / 3.2 x 10⁴

= .3125 x 10⁻⁴

=3.125 x 10⁻⁵ Ω m

User FrengoF
by
5.3k points