Posts in Circuits 1
Phasors and the Unit Circle

Today we’re going to confront a simple lie you learned in high school, and replace it with something more complicated.  The topic today is the unit circle. Personally, I don’t see that many uses for the unit circle, aside from teaching students how to deal with trig identities and right triangles.  But the unit circle become much more interesting when you use it to describe imaginary numbers.

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Single Ideal Op Amp Circuit

Before we start the problem, we should go over a couple things about op amps that’ll help us solve the problem and check our work. For one, notice how the resistor for Vo is connected to the negative terminal of the op amp (not directly, as it goes through the 63 k-ohm resistor, but you could draw a line between Vo and the negative terminal without making a new wire). This means that the op amp is undergoing negative feedback (NFB).

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Mesh Analysis with Supermesh

The first thing you should notice about this circuit is that there are two different types of sources: a dependent source (the arrow in the diamond), and an independent source (the arrow in the circle). Independent sources are independent of the circuit--so that source will always push 15 A of current into the circuit, regardless of the circuit elements.

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Nodal Analysis

Find the value of the voltage v in the circuit below.

The first thing you should notice is the two different types of sources (current sources are the ones with arrows in the middle of them, voltage sources are the ones with the plus and minus). The 5 ampere current source (the arrow with a circle around it) and the 16 volt voltage source (the circle with a plus and minus in it), are independent sources.

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