27. Resistors & DC Circuits

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?

Which of the following is true about the change in potential across a resistor in a circuit?

A copper transmission cable 100 km long and 10.0 cm in diameter carries a current of 125 A. (b) How much electrical energy is dissipated as thermal energy every hour?

(b) What is the resistance of a carbon rod at 25.8°C if its resistance is 0.0160 Ω at 0.0°C?

A hollow aluminum cylinder is 2.50 m long and has an inner radius of 2.75 cm and an outer radius of 4.60 cm. Treat each surface (inner, outer, and the two end faces) as an equipotential surface. At room temperature, what will an ohmmeter read if it is connected between (a) the opposite faces and (b) the inner and outer surfaces?

In household wiring, copper wire 2.05 mm in diameter is often used. Find the resistance of a 24.0-m length of this wire.

A ductile metal wire has resistance R. What will be the resistance of this wire in terms of R if it is stretched to three times its original length, assuming that the density and resistivity of the material do not change when the wire is stretched? (Hint: The amount of metal does not change, so stretching out the wire will affect its cross-sectional area.)

A cylindrical tungsten filament 15.0 cm long with a diameter of 1.00 mm is to be used in a machine for which the temperature will range from room temperature (20°C) up to 120°C. It will carry a current of 12.5 A at all temperatures. (c) What will be the maximum potential drop over the full length of the filament?

The circuit shown in Fig. E25.30

contains two batteries, each with an emf and an internal resistance, and two resistors. Find (c) the potential difference Vac of point a with respect to point c.

A 1.5 V battery provides 0.50 A of current. (a) At what rate (C/s) is charge lifted by the charge escalator?

Electrical engineers sometimes use a wire's conductance, G=σA/L, instead of its resistance. c. A 1.5 A current flows through the wire of part b. What is the potential difference between the ends of the wire?

A 0.0075 V/m electric field creates a 3.9 mA current in a 1.0-mm-diameter wire. What material is the wire made of?

(a) How long must a 0.60-mm-diameter aluminum wire be to have a 0.50 A current when connected to the terminals of a 1.5 V flashlight battery?

The femoral artery is the large artery that carries blood to the leg. What is the resistance of a 20-cm-long column of blood in a 1.0-cm-diameter femoral artery? The conductivity of blood is 0.63 Ω⁻¹ m⁻¹.

FIGURE EX27.35 is a current-versus-potential-difference graph for a material. What is the material's resistance?

The resistance of a very fine aluminum wire with a 10 μm ×10 μm square cross section is 1000 Ω . A 1000 Ω resistor is made by wrapping this wire in a spiral around a 3.0-mm-diameter glass core. How many turns of wire are needed?

Thermistors, resistors whose resistance is a sensitive function of temperature, are widely used in industry and consumer devices to measure temperature. The resistance of a thermistor at temperature T can be modeled as R=R₀exp[β(1/T−1/T₀)], where T₀ is a reference temperature, the temperatures are in K, and β is a constant with units of K. Suppose you connect a thermistor to a 10.0 V battery and measure the current through it at different temperatures. At 25.0°C, which you select as your reference temperature, the current is 10.0 mA. b. Raising the temperature to 30.0°C causes the current to increase to 12.5 mA. What is the value of β?

The resistivity of a metal increases slightly with increased temperature. This can be expressed as ρ=ρ₀[1+α(T−T₀)] , where T₀ is a reference temperature, usually 20°C, and α is the temperature coefficient of resistivity. b. For copper, α=3.9×10^−3 °C^−1. Suppose a 2.5-m-long, 0.40-mm-diameter copper wire is connected across the terminals of a 1.5 V ideal battery. What is the current in the wire at 20°C?

A hollow metal cylinder has inner radius a, outer radius b, length L, and conductivity σ. The current I is radially outward from the inner surface to the outer surface. b. Evaluate the electric field strength at the inner and outer surfaces of an iron cylinder if a=1.0 cm, b=2.5 cm, L=10 cm, and I=25 A.

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. b. You don't want the potential difference between the top and bottom of the lightning rod to exceed 100 V. What minimum diameter must the rod have?

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?

An engineer cuts a 1.0-m-long, 0.33-mm-diameter piece of wire, connects it across a 1.5 V battery, and finds that the current in the wire is 8.0 A. Of what material is the wire made?

Variations in the resistivity of blood can give valuable clues about changes in various properties of the blood. Suppose a medical device inserts microelectrodes into a 1.5-mm-diameter vein at positions 5.0 cm apart. What is the blood resistivity if a 9.0 V potential difference causes a 230 μA current through the blood in the vein?

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?

Electrical engineers sometimes use a wire's conductance, G=σA/L, instead of its resistance. b. What is the conductance of a 5.4-cm-long, 0.15-mm-diameter tungsten wire?

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 scientist measuring the resistivity of a new metal alloy left her ammeter in another lab, but she does have a magnetic field probe. So she creates a 6.5-m-long, 2.0-mm-diameter wire of the material, connects it to a 1.5 V battery, and measures a 3.0 mT magnetic field 1.0 mm from the surface of the wire. What is the material's resistivity?