A wire of length L and resistivity p has a circular cross section with a diameter that tapers linearly from d at one end to zero (a point ideally) at the other end. Derive a formula for the electrical resistance along the length of the wire. (Note: The cross-sectional area changes along the length).

A wire of length L and resistivity p has a circular cross section with a diameter that tapers linearly from d at one end to zero (a point ideally) at the other end. Derive a formula for the electrical resistance along the length of the wire. (Note: The cross-sectional area changes along the length).

Inquiry into Physics

8th Edition

ISBN:9781337515863

Author:Ostdiek

Publisher:Ostdiek

Chapter7: Electricity

Section: Chapter Questions

Problem 4C: Using your understanding of the nature of internal energy and temperature, explain why we might...

See similar textbooks

Similar questions

Using your understanding of the nature of internal energy and temperature, explain why we might expect the resistance of a solid to increase if its temperature increases.
(Indicates a review question, which means it requires only a basic understanding of the material to answer. Questions without this designation typically require integrating or extending the concepts presented thus far.) . Six resistors, all having the same temperatures and compositions, are each attached to a battery with voltage V to form a simple circuit. The resistors have different lengths, l, but the same diameters. Rank the circuits according to the current that flows through the resistor from smallest to greatest. If two (or more) circuits have the same current flowing, give them the same ranking. Explain the rationale you used to establish your rankings. Circuit 1: l = 2 cm; V = 3 V Circuit 2: l = 2 cm; V = 6 V Circuit 3: l = 1 cm; V = 3 V Circuit 4: l = 1 cm; V = 6 V Circuit 5: l = 3cm; V = 2 V Circuit 6: l = 3cm; V = 6 V
An electronic device designed to operate at any temperature in the range from 10.0C to 55.0C contains pure carbon resistors. By what factor does their resistance increase over this range?
Check Your Understanding How would you use a river and two waterfalls to model a parallel configuration of two resistors? How does this analogy break down?
Equation P = I2R Seems to suggest that rate of increase of internal energy in a resistor is reduced, if the resistance is made less. Equation P = V2/R seams to suggest just the opposite. How do you reconcile this apparent paradox?
I = V/R What is the nature of resistance when current decreases? I don't understand how the resistence is being applied.
Pleaseee calculate the resistance, suggest one way and explain in details
As the potential across the resistor increased, the current through the resistor increased. If thechange in current is proportional to the potential difference, the data should be in a straight lineand the y-intercept should be zero. In the two resistor examples how close is the y-intercept tozero? Is there a proportional relationship between potential difference and current? If so, writethe equation for each resistor data set in the form V = mI. Use a numerical value for theproportionality constant, m. Compare the constant in each of the above equations to the resistance of each resistor.
Given n resistors each of resistance R, how will you combine them to get the (i) maximum (ii) minimum effective resistance? What is the ratio of the maximum to minimum resistance?
The interior of thehuman body has an electrical resistivity of 0.15 Ω # m. (a) Estimatethe resistance for current flowing the length of your index finger.(For this calculation, ignore the much higher resistivity of yourskin.) (b) Your muscles will contract when they carry a currentgreater than 15 mA. What voltage is required to produce this current through your finger?
A heater consists of a variable resistor (a resistor whose resistance can be varied)connected across an ideal voltage supply. To increase the heat output, should you decreasethe resistance or increase the resistance? Explain your answer. (b) A 9-μF capacitor ischarged through a 15-k Ω resistor by a 220-V power supply. How long does it require forthe capacitor to acquire 89 percent of its final charge?
A wire of length L and cross-sectional area A has resistance R. What will be the resistance Rstretched of the wire if it is stretched to twice its original length? Assume that the density and resistivity of the material do not change when the wire is stretched.