Question

The current through a 10 m long wire has a current density of 4 cross times 10 to the power of 6 space open parentheses bevelled A over m squared close parentheses. The wire conductivity is 2 cross times 10 to the power of 7 space open parentheses bevelled S over m close parentheses. Find the voltage drop across the wire. (Answer with the numeric value, don't write the unit V)

Answer 1

The voltage drop across the wire is 2 V

Step-by-step explanation:

Given;

length of wire, L = 10 m

current density, I/A, μ = 4 x 10⁶ (A/m²)

wire conductivity, σ = 2 x 10⁷ (S/m)

The resistivity of wire is given by;

`\rho = (RA)/(L) \\\\But \ R = V/I\\\\\rho = (VA)/(IL)`

Conductivity, σ = ¹/ρ

`\sigma = (IL)/(VA)\\ \\V = (IL)/( A \sigma)\\\\V = ((I)/(A))(L)/(\sigma)\\ \\V = (\mu)(L)/(\sigma)\\\\V = (4*10^(6) )*(10)/(2*10^(7) ) \\\\V = 2 \ V`

Therefore, the voltage drop across the wire is 2 V