A rectangular piece of gold is 3.1 cm long and 3 cm wide. Resistivity of gold is 2.4*10^-8. How deep is the piece when it displays a resistance of R = 1.65 μω for a current that flows along the depth-direction?
I used R=(p*l)/A and solved for l. I got the answer wrong. For the area I used 0.03*0.03 as the cross sectional area. What did I do wrong?
The area is 0.03 * d, and you are supposed to solve for d, knowing the total resistance. Current flow is along the length, which you know to be 3.1 cm.
There is possibly another problem as well. The resistivity of gold is approximately 2.44 × 10-8 ohm-m. The way you are using it, with gold block dimensions in cm, you have to change the value of p to 2.44 × 10-6 ohm-cm
Thank you.
To find the depth, you correctly used the formula R = (ρ * l) / A, where R is the resistance, ρ is the resistivity, l is the length, and A is the cross-sectional area.
The mistake you made is in the calculation of the cross-sectional area. The given dimensions of the rectangular piece of gold are 3.1 cm (length) and 3 cm (width). However, the depth or thickness is not mentioned.
To calculate the cross-sectional area, you need to multiply the length and width values. In this case, you would multiply 3.1 cm by 3 cm. However, since you need to find the depth, the multiplication of length and width would give you the total volume, not the cross-sectional area.
To obtain the correct cross-sectional area, you need to know either the depth of the gold piece, or you need more information about the shape of the piece that can help determine the depth.
Once you have the correct cross-sectional area, you can rearrange the formula as follows to solve for the depth:
l = (R * A) / ρ
Therefore, to find the correct depth, you either need to know the depth of the gold piece or have additional information about its shape.