27. Resistors & DC Circuits

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?

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. 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. 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. 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.

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?

Electrical engineers sometimes use a wire's conductance, G=σA/L, instead of its resistance. 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. 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?

An idealized ammeter is connected to a battery as shown in Fig. E$25.28$. Find the terminal voltage of the battery.

An idealized ammeter is connected to a battery as shown in Fig. E$25.28$. Find the current through the $4.00$-$\Omega$ resistor.

An idealized ammeter is connected to a battery as shown in Fig. E$25.28$. Find the reading of the ammeter.