5) Consider a circuit in which sinusoidal current i(t) of amplitude I, frequency f, and initial phase angle 0 flows; that is, i(t)  I sin(2ft  0 ) . Derive an expression for the voltage vL(t) across an inductor of inductance L through which that current flows. Based on your derivation, how should inductor voltage amplitude VL (i. e., the amplitude of the voltage across the inductor) vary with frequency? Describe the phase of the inductor voltage vL(t) relative to the current in the circuit.

What happens to light waves from a star as the star moves away from earth?

Name three different units of energy used to measure heat and describe what type of situations each is usually used.

Three different objects, all with different masses, are initially at rest at the bottom of a set of steps. each step is of uniform height . the mass of each object is a multiple of the base mass : object 1 has mass 4..00m , object 2 has mass 1..96m , and object 3 has mass . when the objects are at the bottom of the steps, define the total gravitational potential energy of the three-object system to be zero. if the objects are then relocated as shown, what is the new total potential energy of the system? each answer requires the numerical coefficient to an algebraic expression. each algebraic expression is given using some combination of the variables , , and , where is the acceleration due to gravity. enter only the numerical coefficient. (example: if the answer is 1..23mgd , just enter 1.23)