The Resistance $R$ Of a Wire Varies Directly as Its Length $L$

question 140

Essay

The resistance $R$ of a wire varies directly as its length $L$ and inversely as the square of twice its radius.
(a) Write an equation that expresses this direct variation.
(b) Find the constant of proportionality if a wire $2.4$ m long and
$0.004$ m in diameter has a resistance of
$150$ ohms.
(b), find the diameter of a wire that has a resistance of $90$ ohms and is
$1.2$ m long.
(c) Using the constant of proportionality from part

---

Definitions:

Morphine Sulfate

A potent opioid analgesic drug used to relieve severe pain by acting directly on the central nervous system.

Cheyne-Stokes Respirations

A pattern of breathing that cycles between deep, rapid breaths and periods of apnea, often associated with heart failure or brain injuries.

Biot's Breathing

A pattern of breathing characterized by groups of quick, shallow breaths followed by regular or irregular periods of apnea; often associated with brain damage or brain pressure.

Kussmaul's Respirations

A pattern of deep, labored breathing often associated with severe metabolic acidosis, particularly diabetic ketoacidosis.