Two resistors are made of the same material, one twice as long as the other. If the current through the shorter resistor is 5 A, what is the current through the longer resistor if they both have the same potential difference and cross-sectional area?

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?

A hollow copper sphere has inner radius 1.0 cm and outer radius 2.5 cm. A 5.0 A current flows radially outward from the inner surface to the outer surface. What is the electric field strength at r=2.0 cm?

A 12 V car battery dies not so much because its voltage drops but because chemical reactions increase its internal resistance. A good battery connected with jumper cables can both start the engine and recharge the dead battery. Consider the automotive circuit of FIGURE P28.64.b. How much current is the dead battery alone able to drive through the starter motor?

A wire runs from the positive plate of a capacitor, into lightbulb 1, then out from lightbulb 1 directly into lightbulb 2. When lightbulb 2 is connected to the negative plate of the capacitor, what is true about the charge moving through the two lightbulbs?

A copper wire with a radius of $2.0\mathrm{ mm}$ and a length of $0.80\mathrm{ m}$ is connected across the terminals of a $9.0\mathrm{V}$ battery. How much current flows in the wire?

A certain wire has length L and radius r, and a resistance of R. That wire is melted down and the same volume of the same metal is used to produce a wire with length 2L. What is the resistance of the resulting wire?

A copper wire and an aluminum wire have the same diameter. If the copper wire is $10\mathrm{ m}$long, how long is the aluminum wire if they have the same resistance?