HW 4 ... more information

Problem 1: the power in a circuit element is in general current times voltage. Using Ohm's law, for a single resistor we can write this as

P=I^2R

The total power in the circuit is the sum of the power in the two resistors,

P=I_1^2R_1+I_2^2R_2

Using the conservation of charge equation, you can put power in terms of the current in a single resistor. Minimize.

Problem 2: now the resistors are in series, the internal resistance r and the external "load" resistance R. You can easily figure out the current through both resistors in this case, and again find the power in each resistor using the formula above. Maximize with respect to R.

Problem 3: see previous post; we'll do some more examples of Thevenin equivalents tomorrow.

Problem 4: break the cone up into tiny disks. If the current is running along the axis of the disk, the resistance of a tiny disk of radius r and thickness dx is

dR = \rho\,dx/\pi r^2

The radius is position-dependent for a cone, you might write it as

r=a+(b-a)x/l

in this case. Integrate over all such disks with resistance dR to find the total R. We'll set up a similar problem in class tomorrow.