Exam 24: Current, Resistance, and Electromotive Force

Building codes usually limit the current carried by a No. 14 copper wire to 15 A. Many household circuits are wired with this size wire. What is the drift velocity of the electrons in this case? The diameter of this wire is 1.6 mm. Assume one conduction electron per atom in copper. The atomic weight of copper is 63.3 g/mol and its density is 8900 kg/m³. Avogadro's number is 6.022 × 10²³ molecules/mol and e = 1.60 × 10^-19 C.

The emf and the internal resistance of a battery are shown in the figure. If a current of 7.8 A is established through the battery from b to a, what is the terminal voltage V_ab of the battery?

What length of a certain metal wire of diameter 0.15 mm is needed for the wire to have a resistance of 15 Ω? The resistivity of this metal is 1.68 × 10^-8 Ω ∙ m.

A certain fuse "blows" if the current in it exceeds 1.0 A, at which instant the fuse melts with a current density of 620 A/cm². What is the diameter of the wire in the fuse?

A light bulb is connected to a 110-V source. What is the resistance of this bulb if it is a 100-W bulb?

When a potential difference of 10 V is placed across a certain solid cylindrical resistor, the current through it is 2 A. If the diameter of this resistor is now tripled, the current will be

The voltage and power ratings of a particular light bulb, which are its normal operating values, are 110 V and 60 W. Assume the resistance of the filament of the bulb is constant and is independent of operating conditions. If the light bulb is operated with a current that is 50% of the current rating of the bulb, what is the actual power drawn by the bulb?

Calculate the current through a 10.0-m long 22 gauge (having radius 0.321 mm) nichrome wire if it is connected to a 12.0-V battery. The resistivity of nichrome is 100 × 10^-8 Ω ∙ m.

A tube of mercury with resistivity 9.84 × 10^-7 Ω ∙ m has an electric field inside the column of mercury of magnitude 23 N/C that is directed along the length of the tube. How much current is flowing through this tube if its diameter is 1.0 mm?

A Nichrome wire is used as a heating element in a toaster. From the moment the toaster is first turned on to the moment the wire reaches it maximum temperature, the current in the wire drops by 20.0% from its initial value. What is the temperature change in the wire? The temperature coefficient of resistivity for Nichrome is 0.000400 (°C)^-1.

A certain electric furnace consumes 24 kW when it is connected to a 240-V line. What is the resistance of the furnace?

The voltage and power ratings of a particular light bulb, which are its normal operating values, are 110 V and 60 W. Assume the resistance of the filament of the bulb is constant and is independent of operating conditions. If the light bulb is operated at a reduced voltage and the power drawn by the bulb is 36 W, what is the operating voltage of the bulb?

The resistivity of gold is 2.44 × 10^-8 Ω ∙ m at room temperature. A gold wire that is 1.8 mm in diameter and 11 cm long carries a current of 170 mA. How much power is dissipated in the wire?

The diameter of a 12-gauge copper wire is 0.081 in. The maximum safe current it can carry (in order to prevent fire danger in building construction) is 20 A. At this current, what is the drift velocity of the electrons? The number of electron carriers in 1.0 cm³ of copper is 8.5 × 10²² and e = 1.60 × 10^-19 C.

A 400-W computer (including the monitor) is turned on for 8.0 hours per day. If electricity costs 10¢ per kWh, how much does it cost to run the computer annually for a typical 365-day year?

In a certain electroplating process gold is deposited by using a current of 14.0 A for 19 minutes. A gold ion, Au+, has a mass of approximately 3.3 × 10^-22 g. How many grams of gold are deposited by this process?

In the figure, when the terminal voltage V_ab of the battery is equal to 20 V, how much current passes through the battery, including its direction?

In an electroplating process, copper (ionic charge +2e, atomic weight 63.6 g/mol) is deposited using a current of 10.0 A. What mass of copper is deposited in 10.0 minutes? Avogadro's number is 6.022 × 10²³ molecules/mol and e = 1.60 × 10^-19 C.

When electric current is flowing in a metal, the electrons are moving

As current flows through a uniform wire, the wire gets hotter because the electrons stop moving and therefore transform their lost kinetic energy into thermal energy in the wire.