Here's the question...
A rectangular solid made of carbon has sides lying along the x, y, and z axes, whose lengths are 1.06 cm, 2.12 cm, and 4.24 cm, respectively, as seen in figure below. Determine the resistance for current that flows through the solid in the x direction. Assume the resistivity is r = 3.00E-5 W* m.
I got various numbers as answers, and used the formula: R = (row)(L/A) where row is resistivity, in this case 3E-5, L is length (x axis, in this case) and A is surface area of a rectangle. Where am I going wrong?!
THANKS!
oh, the resistivity is omega (ohms)*m, not W. sorry!
To determine the resistance for current that flows through the solid in the x direction, you are on the right track by using the formula: R = ρ (L/A), where ρ is the resistivity, L is the length, and A is the cross-sectional area.
However, in this case, you need to be careful with choosing the correct values for L and A. The given dimensions of the rectangular solid are along the x, y, and z axes, and you are only interested in the resistance in the x direction.
To calculate the resistance for current that flows through the solid in the x direction, you need to consider the dimensions of the rectangular solid for the x direction only.
Given:
Length along the x-axis (Lx) = 1.06 cm
To find the cross-sectional area in the x direction (Ax), you need to consider the y and z dimensions, as they are perpendicular to the x direction.
Given:
Length along the y-axis (Ly) = 2.12 cm
Length along the z-axis (Lz) = 4.24 cm
To determine the cross-sectional area in the x direction, you need to multiply Ly and Lz, which gives:
Ax = Ly * Lz = 2.12 cm * 4.24 cm
Now, convert the length and area to meters since the resistivity ρ is given in ohm-meter:
1 cm = 0.01 m
Lx = 1.06 cm * 0.01 m/cm
Ax = 2.12 cm * 0.01 m/cm * 4.24 cm * 0.01 m/cm
Now, substitute these values into the resistance formula:
R = ρ (Lx/Ax)
R = (3.00E-5 Ω*m) * (1.06 cm * 0.01 m/cm) / (2.12 cm * 0.01 m/cm * 4.24 cm * 0.01 m/cm)
Simplifying the expression:
R = (3.00E-5 Ω*m) * (0.0106 m) / (0.090064 m^2)
Now, calculate the value of R:
R ≈ 3.55E-3 Ω
So, the resistance for the current that flows through the solid in the x direction is approximately 3.55 milliohms.