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08:30A 300 μF capacitor is charged to 9.0 V, then connected in parallel with a 5000 Ω resistor. The capacitor will discharge because the resistor provides a conducting pathway between the capacitor plates, but much more slowly than if the plates were connected by a wire. Let t=0 s be the instant the fully charged capacitor is first connected to the resistor. At what time has the capacitor voltage decreased by half, to 4.5 V?
A 2.0-mm-diameter wire formed from a composite material has a resistivity that decreases with distance along the wire as ρ=ρ₀e−αx, where ρ₀=4.0×10−5 Ω m, x (in m) is measured from one end of the wire, and the constant α=4.0 m−1. What is the resistance of a 50-cm-long length of this wire?
You've decided to protect your house by placing a 5.0-m-tall iron lightning rod next to the house. The top is sharpened to a point and the bottom is in good contact with the ground. From your research, you've learned that lightning bolts can carry up to 50 kA of current and last up to 50 μs. How much charge is delivered by a lightning bolt with these parameters?
An aluminum wire consists of the three segments shown in FIGURE P27.64. The current in the top segment is 10 A. For each of these three segments, find the current density J. Place your results in a table for easy viewing.
Two 10-cm-diameter metal plates 1.0 cm apart are charged to ±12.5 nC. They are suddenly connected together by a 0.224-mm-diameter copper wire stretched taut from the center of one plate to the center of the other. Does the current increase with time, decrease with time, or remain steady? Explain.
An aluminum wire consists of the three segments shown in FIGURE P27.64. The current in the top segment is 10 A. For each of these three segments, find the drift velocity vd. Place your results in a table for easy viewing.
