20.309: Biological Instrumentation and Measurement
This is Part 2 of Assignment 6.
Resistive circuits

For each of the circuits below, find the voltage at each node and the current through each element. You do not have to simplify your answer. (You may leave in terms such as R1R2.) You might be able to dramatically simplify your calculations using equivalent circuits.

Equivalent circuits

For each of the circuits in the previous problem, find two equivalent circuits — the first one consisting of a single voltage source and a single resistor, and the second one consisting of one current source and one resistor. In both equivalent circuits, the IV curve at the V_{out} the port should be identical to the original circuit.

Ideal elements

For each of the ideal, twoterminal elements listed below, show the symbol, label the terminals, indicate the direction of current flow, write the constitutive equation, and find an expression for the impedance, $ Z(\omega)=\frac{V}{I} $. (To find the impedance, substitute $ V=Ae^{j\omega t} $ into the constitutive equation and solve for $ \frac{V}{I} $ as a function of $ \omega $.)
 Resistor
 Capacitor
 Inductor
 Voltage source
 Current source

Bode plots
Make a bode magnitude and phase plot for the circuit below.