A teacher is concerned about accidentally tripping his mercury alarm with a giant solenoid you build for him and has asked you to determine how much power is dissipated as heat by the wires of the solenoid. The resistivity of copper is 1.68 × 10−8 Ω·m. Side note: the solenoid is one layer of tightly-wrapped 12-gauge copper wire (diameter is 0.2032 mm). It is to be 3.5 meters tall and square in shape with 0.75-m long sides.

An electric eel generates electric currents through its highly specialized Hunters organ, in which thousands of disk-shaped cells called electrocytes are lined up in series, very much in the same way batteries are lined up inside a flashlight. When activated, each electrocyte can maintain a potential difference of about 150 mV at a current of 1.0 A for about 2.0 ms. Suppose a grown electric eel has 4.0 103 electrocytes and can deliver up to 3.00 102 shocks in rapid series over about 1.0 s. (a) What maximum electrical power can an electric eel generate? (b) Approximately how much energy does it release in one shock? (c) How high would a mass of 1.0 kg have to be lifted so that its gravitational potential energy equals the energy released in 3.00 102 such shocks?

At one instant, a current of 6.0 A flows through part of a circuit as shown in Figure P33.12. Determine the instantaneous potential difference between points A and B if the current starts to decrease at a constant rate of 1.0 102 A/s. FIGURE P33.12

Unreasonable Results (a) What current is needed to transmit 1.00 102 MW of power at 10.0kV? (b) Find the resistance of 1.00 km of wire that would cause a 0.0100% power loss. (c) What is the diameter of a 1.00-km-long copper wire having this resistance? (d) What is unreasonable about these results? (e) Which assumptions are unreasonable, or which premises are inconsistent?

Explain why R=R0(1 + a?T) for the temperature variation of the resistance R of an object is not as accurate as P=P0(1 + a?T) which gives the temperature variation of resistivity P.

(a) Find the current in each resistor of Figure P18.18 by using the rules for resistors in series and parallel. (b) Write three independent equations for the three currents using Kirchhoffs laws: one with the node rule; a second using the loop rule through the battery, the 6.0- resistor, and the 24.0- resistor; and the third using the loop rule through the 12.0- and 24.0- resistors. Solve to check the answers found in part (a). Figure Pl8.18

You are working with an oceanographer who is studying how the ion concentration in seawater depends on depth. She shows you the device that she uses to measure the resistivity of water from a boat. It consists of a pair of concentric metallic cylinders at the end of a cable (Fig. P26.36). Seawater flows freely between the two cylindrical shells. She makes a measurement by lowering the device into the water and applying a potential difference V between the inner and outer cylinders. This produces an outward radial current I in the seawater between the shells. She shows you the current and voltage data for the water at a particular depth and is then called away to answer a long call on her cellphone about a laboratory issue back on the mainland. As she leaves, she says, Have the resistivity of the water calculated when I get back. She forgot to show you any tables or formulas to use to determine the resistivity, so you are on your own. Quick! Find an expression for the resistivity in terms of I and V before she finishes her phone call! Figure P26.36

The emfs in Figure P29.43 are 1 = 6.00 V and 2 = 12.0 V. The resistances are R1 = 15.0 , R2 = 30.0 , R3 = 45.0 , and R4 = 60.0 . Find the current in each resistor when the switch is a. open and b. closed.

Taking R = 1.00 k and = 250 V in Figure P21.49, determine the direction and magnitude of the current in the horizontal wire between a and e. Figure P21.49

The temperature near the center of the Sun is thought to be 15 million degrees Celsius ( 1.5107oC ) (or kelvin). Through what voltage must a singly charged ion be accelerated to have the same energy as the average kinetic energy of ions at this temperature?