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Solved: CALC A 1.50-m cylinder of radius 1.10 cm is made
Chapter 25, Problem 76P(choose chapter or problem)
A 1.50-m cylinder of radius 1.10 cm is made of a complicated mixture of materials. Its resistivity depends on the distance x from the left end and obeys the formula \(\rho(x)=a+b x^{2}\), where a and b are constants. At the left end, the resistivity is \(2.25 \times 10^{-8} \Omega \cdot \mathrm{m}\), while at the right end it is \(8.50 \times 10^{-8} \Omega \cdot \mathrm{m}\)
(a) What is the resistance of this rod?
(b) What is the electric field at its midpoint if it carries a 1.75-A current?
(c) If we cut the rod into two 75.0-cm halves, what is the resistance of each half?
Questions & Answers
QUESTION:
A 1.50-m cylinder of radius 1.10 cm is made of a complicated mixture of materials. Its resistivity depends on the distance x from the left end and obeys the formula \(\rho(x)=a+b x^{2}\), where a and b are constants. At the left end, the resistivity is \(2.25 \times 10^{-8} \Omega \cdot \mathrm{m}\), while at the right end it is \(8.50 \times 10^{-8} \Omega \cdot \mathrm{m}\)
(a) What is the resistance of this rod?
(b) What is the electric field at its midpoint if it carries a 1.75-A current?
(c) If we cut the rod into two 75.0-cm halves, what is the resistance of each half?
ANSWER:Step 1 of 5
The resistance of the conductor is directly proportional to the length of the conductor and inversely proportional to cross sectional area.
