A slab of metal of volume V is made into a rod of length L. The rod carries current I when the electric field inside is E.Find the resistivity of the metal?
NVM again sorry I solved it.
The cross sectional area of the rod is A = V/L. The resistance of the rod is
R = (resistivity)*L/A
= (resistivity)*L^2/V
I = V/R = E*L/R,
= E*L*V/(resistivity)*L^2
= E*V/[resistivity*L]
Solve for resisitivity
The rod is now stretched so that its length is doubled. If the electric field remains the same, what is the new current I' in the rod? The answer to the first part was (EV)/(IL)
If you double the length, the area decreases by a factor 1/2. In this case you keep the E field the same and not the voltage. Voltage doubles. Resistance increases by a factor of 4. the current therefore decreases by a factor of two.
You can also see this from your formula. resistivity, E, and V are constant, so I is inversely proportional to L.
Thank you phew I got it done on time
A piece of copper is made into a rod with a square cross-section. The side of the square is 2.00 centimeters. The resistivity of copper is 1.7 \cdot 10^{-8} \Omega\cdot {\rm m}. An unknown electric field E, directed along the rod, creates a current of 12.0 amperes through the rod. Find the magnitude of E.
kjlk
1)
let:
V = change in V
E = electric field
I = current
L = length of rod
A = square cross-section
R = resistance
given equations (from physic):
E = V / L
I = V / R
R = rho * L /A
by that:
E*L =V
IR =V
R = rho *L /A
EL = I * rho * L /A
E = I * rho /A
E = 12 * 1.7e-8 / (2/100)^2
= 5.1e-4
To find the resistivity of the metal, we can use the formula relating resistivity (ρ), electric field (E), current (I), and dimensions of the conductor.
The formula is:
ρ = (E * L) / (I * A)
Where:
ρ is the resistivity of the metal
E is the electric field inside the rod
L is the length of the rod
I is the current flowing through the rod
A is the cross-sectional area of the rod
Now, we need to find the cross-sectional area of the rod, which was originally a slab of volume V.
To find the cross-sectional area, we need to know the initial shape of the slab. If the slab is a rectangular shape, with length L and width W, then the cross-sectional area (A) of the rod is A = L * W.
Once we know the cross-sectional area (A), we can substitute the given values into the formula to find the resistivity (ρ) of the metal.