FRQ ELECTRICITY $3-1-24$

$6.$ Read each question carefully. Show all your work for each part of the question. The parts within the question may not have equal weight.

A cylinder of length $L=0\mathrm{.}25m$ and radius $r=0\mathrm{.}020m$ is made of two different materials, as sujwn. The top half has a resistivity of ${}_1=0\mathrm{.}46*m,$ and the bottom half has a resistivity of ${}_2=0\mathrm{.}92*m.$ The cylinder has connection wires at the center of each end, as shown.

$($a$)$ Calculate the resistance of this cylinder.

$($b$)$ The cylinder from part $($a$)$ is placed into the circuit shown above in which the dashed rectangular area represents the cylinder. The rest of the circuit consists of a variable voltage source with potential difference $,$ ideal meters $M_1$ and $M_2,$ switch $S,$ and a resistor of known resistance $R_0.$ The switch is closed, and a current I measured for the circuit.

i$.$ Which of the following indicates the measurement made by meter $M_1?$ Check all that apply.

Potential difference across the cylinder

Potential difference across resistor $R_0$

Potential difference of the voltage source

Current through the cylinder

Current through resistor $R_0$

Current through the voltage source