a conductor is 2m long and 8mm diameter if its resistivity is 1.8*10^-8 ohmm calculate
a,the resistance of the conductor
b,the current in the conductor when a p.d of 10v is maintained across its ends
c,the current density
d,the electric field in the wire
L=2 m,
s=πr² = π(8*10⁻³)² =64π*10⁻⁶ m²,
ρ=1.8*10⁻⁸Ohm•m.
a. R= ρL/s
b. I=U/R
c. j=I/s
d. the charges are on the surface
of the wire => the electric in the wire is zero
To calculate the required values, we need to use some formulas and concepts from physics. Let's start with the given information:
Length of the conductor (L) = 2 m
Diameter of the conductor (d) = 8 mm = 8 x 10^-3 m
Resistivity (ρ) = 1.8 x 10^-8 ohm meter (Ωm)
Potential Difference (V) = 10 V
a) Resistance of the conductor:
Resistance (R) can be calculated using the formula:
R = (ρ x L) / A
Where A is the cross-sectional area of the conductor. We can find A using the formula:
A = π x (d/2)^2
Let's substitute the given values into the formulas:
A = π x (8 x 10^-3 / 2)^2 = 3.14 x (4 x 10^-3)^2 = 3.14 x 16 x 10^-6 = 50.24 x 10^-6 m^2
R = (1.8 x 10^-8 x 2) / (50.24 x 10^-6)
R = 0.36 x 10^-8 / 50.24 x 10^-6
R = 0.007155 Ω (approximately)
So, the resistance of the conductor is approximately 0.007155 Ω.
b) Current in the conductor:
We can use Ohm's law to calculate the current (I):
I = V / R
Let's substitute the given values into the formula:
I = 10 / 0.007155
I ≈ 1397.32 A (approximately)
So, the current in the conductor when a potential difference of 10 V is applied across its ends is approximately 1397.32 A.
c) Current Density:
Current density (J) is defined as the current per unit area. It can be calculated using the formula:
J = I / A
Let's substitute the values we have calculated:
J = 1397.32 / 50.24 x 10^-6
J ≈ 27,785 A/m² (approximately)
So, the current density in the conductor is approximately 27,785 A/m².
d) Electric Field in the wire:
The electric field (E) can be calculated using Ohm's law formula:
E = V / L
Let's substitute the given values into the formula:
E = 10 / 2
E = 5 V/m
So, the electric field in the wire is 5 V/m.