9.6 Superconductors

What requirement for superconductivity makes current superconducting devices expensive to operate?

Consider a power plant is located 60 km away from a residential area uses 0-gauge $\left(A = 42.40 \text{mm}^{2}\right)$ wire of copper to transmit power at a current of $I = 100.00 \text{A}$. How much more power is dissipated in the copper wires than it would be in superconducting wires?

Digital medical thermometers determine temperature by measuring the resistance of a semiconductor device called a thermistor (which has $\alpha = −0.06 / ° \text{C}$) when it is at the same temperature as the patient. What is a patient’s temperature if the thermistor’s resistance at that temperature is 82.0% of its value at $37 ° \text{C}$ (normal body temperature)?

A 12-gauge gold wire has a length of 1 meter. (a) What would be the length of a silver 12-gauge wire with the same resistance? (b) What are their respective resistances at the temperature of boiling water?

A coaxial cable consists of an inner conductor with radius $r_{\text{i}} = 0.25 \text{cm}$ and an outer radius of $r_{\text{o}} = 0.5 \text{cm}$ and has a length of 10 meters. Plastic, with a resistivity of $\rho = 2.00 \times 10^{13} \Omega \cdot \text{m}$, separates the two conductors. What is the resistance of the cable?

A nichrome rod that is 3.00 mm long with a cross-sectional area of $1.00 \left( \text{mm}\right)^{2}$ is used for a digital thermometer. (a) What is the resistance at room temperature? (b) What is the resistance at body temperature?

When 100.0 V is applied across a 5-gauge (diameter 4.621 mm) wire that is 10 m long, the magnitude of the current density is $2.0 \times 10^{8} \text{A}/\text{m}^{2}$. What is the resistivity of the wire?

What is the resistivity of a wire of 5-gauge wire $\left(\right. A = 16.8 \times 10^{−6} \text{m}^{2}$), 5.00 m length, and $5.10 \text{m} \Omega$ resistance?

Currents of approximately 0.06 A can be potentially fatal. Currents in that range can make the heart fibrillate (beat in an uncontrolled manner). The resistance of a dry human body can be approximately $100 \text{k} \Omega$. (a) What voltage can cause 0.06 A through a dry human body? (b) When a human body is wet, the resistance can fall to $100 \Omega$. What voltage can cause harm to a wet body?

A battery with an emf of 24.00 V delivers a constant current of 2.00 mA to an appliance. How much work does the battery do in three minutes?

A 10-gauge copper wire has a cross-sectional area $A = 5.26 \text{mm}^{2}$ and carries a current of $I = 5.00 \text{A}$. The density of copper is $\rho = 8.95 \left( \text{g}/\text{cm}\right)^{3}$. One mole of copper atoms $\left(6.02 \times 10^{23} \text{atoms}\right)$ has a mass of approximately 63.50 g. What is the magnitude of the drift velocity of the electrons, assuming that each copper atom contributes one free electron to the current?

A particle accelerator produces a beam with a radius of 1.25 mm with a current of 2.00 mA. Each proton has a kinetic energy of 10.00 MeV. (a) What is the velocity of the protons? (b) What is the number (n) of protons per unit volume? (b) How many electrons pass a cross sectional area each second?

A current of $I = 25 A$ is drawn from a 100-V battery for 30 seconds. By how much is the chemical energy reduced?

A resistor of an unknown resistance is placed in an insulated container filled with 0.75 kg of water. A voltage source is connected in series with the resistor and a current of 1.2 amps flows through the resistor for 10 minutes. During this time, the temperature of the water is measured and the temperature change during this time is $\Delta T = 10.00 ° \text{C}$. (a) What is the resistance of the resistor? (b) What is the vo…

A student uses a 100.00-W, 115.00-V radiant heater to heat the student’s dorm room, during the hours between sunset and sunrise, 6:00 p.m. to 7:00 a.m. (a) What current does the heater operate at? (b) How many electrons move through the heater? (c) What is the resistance of the heater? (d) How much heat was added to the dorm room?

A physics student uses a 115.00-V immersion heater to heat 400.00 grams (almost two cups) of water for herbal tea. During the two minutes it takes the water to heat, the physics student becomes bored and decides to figure out the resistance of the heater. The student starts with the assumption that the water is initially at the temperature of the room $T_{i} = 25.00 ° \text{C}$ and reaches $T_{f} = 100.00 ° \text{C}$. The specific heat of the wate…