Question

you are given a rectangular block of an unknown resistive material which is 1.0 cm high by 4.0 cm wide by 6.0 cm long. you measure a resistance of r when electrodes are connected to the top and bottom of the block in order to measure resistance across the height of the block. what is the correct sequence of resistance values that you will measure when the resistance is measured across the width of the block, and finally the length of the block?
o r, 1.5r, 6r
o r, 4r, 6r
o r, 8r, 24r
o r, 16r, 36r

Explanation:

Step1: Recall resistance formula

The resistance formula is $R =
ho\frac{l}{A}$, where $
ho$ is resistivity, $l$ is length, and $A$ is cross - sectional area.

Step2: Calculate resistance when measuring across height

When measuring across the height $h = 1.0\ cm$, $l = h$ and $A=w\times L$ (width $w = 4.0\ cm$ and length $L = 6.0\ cm$), so $R_1=
ho\frac{h}{w\times L}$.

Step3: Calculate resistance when measuring across width

When measuring across the width $w = 4.0\ cm$, $l = w$ and $A = h\times L$, so $R_2=
ho\frac{w}{h\times L}$. Then $\frac{R_2}{R_1}=\frac{
ho\frac{w}{h\times L}}{
ho\frac{h}{w\times L}}=\frac{w^{2}}{h^{2}}=\frac{4^{2}}{1^{2}} = 16$. So $R_2 = 16R$.

Step4: Calculate resistance when measuring across length

When measuring across the length $L = 6.0\ cm$, $l = L$ and $A=h\times w$, so $R_3=
ho\frac{L}{h\times w}$. Then $\frac{R_3}{R_1}=\frac{
ho\frac{L}{h\times w}}{
ho\frac{h}{w\times L}}=\frac{L^{2}}{h^{2}}=\frac{6^{2}}{1^{2}}=36$. So $R_3 = 36R$.

Answer:

R, 16R, 36R