Ohm's law, power

Problem:

A linear accelerator produces a beam of electrons in which the current is not constant but consists of a pulsed beam of particles.  Suppose that the pulse current is 1.6 A for a 0.1 ┬Ás duration. 
(a)  How many electrons are accelerated in each pulse?
(b)  What is the average beam current if there are 1000 pulses per second?
(c)  If the electrons are accelerated to an energy of 400 MeV, what is the average beam power on target?
(d)  What is the peak beam power on target?
(e)  What fraction of the time is the accelerator actually delivering beam on target?  (This is called the duty factor of the accelerator.)

Solution:


Ohm's law, resistance, power

Problem:

Two metallic spheres of the same radius r are immersed in a homogeneous liquid with resistivity ρ.  What is the total resistance between two spheres?  Assume that the distance between two spheres is much larger than the sphere radius.

Problem:

A current I flows through a wire made of a piece of material 1 and a piece of material 2 of identical cross-sections A welded end-to-end as shown in the figure.  The resistivity of material 1 is ρ1, the resistivity of material 2 is ρ2.  How much electric charge accumulates at the boundary between the two materials?

image

Solution:

Problem:

A copper wire (ρ = 1.72*10-8 Ωm) has a length of 160 m and a diameter of 1.00 mm.  If the wire is connected to a 1.5 V battery, how much current flows through the wire?

Solution:

Problem:

A high-voltage transmission line that connects a city to a power plant consists of a pair of copper cables, each with a resistance of 4 W.  The current flows to the city along one cable, and back along the other.
(a)  The transmission line delivers to the city 1.7*105 kW of power at 2.3*105 V.  What is the current in the transmission line?  How much power is lost as Joule heat in the transmission line?
(b)  If the transmission line delivers the same 1.7*105 kW of power at 110 V, how much power would be lost in Joule heat?  Is it more efficient to transmit power at high voltage or at low voltage?

Solution: