Aparallel circuit has three branches. each branch has a resistance of 37.5 ohms. the total current is 7.5 amps. what is the current value of each branch circuit?

Acylinder with a movable piston contains 11.7 moles of a monatomic ideal gas at a pressure of 1.32×10^5 pa. the gas is initially at a temperature of 300 k. an electric heater adds 43200 j of energy into the gas while the piston moves in such a way that the pressure remains constant. cp=20.79 j k^−1 mol^−1 for a monatomic ideal gas, and that the number of gas molecules is equal to avogadro's number (6.022×10^23) times the number of moles of the gas. (a) what is the temperature of the gas after the energy is added? (b) what is the change in volume of the gas? (c) how much work is done by the gas during this process?

Suppose water is leaking from a tank through a circular hole of area ah at its bottom. when water leaks through a hole, friction and contraction of the stream near the hole reduce the volume of water leaving the tank per second to cah 2gh , where c (0 < c < 1) is an empirical constant. a tank in the form of a right-circular cone standing on end, vertex down, is leaking water through a circular hole in its bottom. (assume the removed apex of the cone is of negligible height and volume.) (a) suppose the tank is 20 feet high and has radius 8 feet and the circular hole has radius 2 inches. the differential equation governing the height h in feet of water leaking from a tank after t seconds is dh dt = − 5 6h3/2 . if the height of the water is initially 8 feet, how long will it take the tank to empty? (round your answer to two decimal places.)

Global warming will produce rising sea levels partly due to melting ice caps but also due to the expansion of water as average ocean temperatures rise. to get some idea of the size of this effect, calculate the change in length of a column of water 1.00 km high for a temperature increase of 1.00ºc. note that this calculation is only approximate because ocean warming is not uniform with depth. (answer in ×10^{-3} −3 m)