A Sloppy Approach to Circuit Analysis
A Sloppy Approach to Circuit Analysis#
Sometimes a desperate man does dumb things.
—Angus MacGyver
Example
Find \(V_S\) if \(P_{R_2}=20~W\).
Solution
\(P_{R_2}\) and \(R_2\) tells you what \(V_{R_2}\) is from
That tells us what \(I_{R_2}\) and \(I_{R_3}\) are, which tells us what \(I_{R_1}\) is.
\(I_{R_1}\) and \(R_1\) tells us \(V_{R_1}\), and KVL then tells us what \(V_S\) is.
Example
Find \(V_\text{6k}\) and \(V_\text{3k}\).
Solution
First, find the equivalent resistance of all the resistors, \(R_{eq}\).
With the \(1 mA\) current supply, that tells us \(V_\text{6k}\).
\(V_\text{3k}\) may then be found using \(V_\text{6k}\) and the voltage divider equation using the equivalent resistance of the two \(4~k\Omega\) resistors and the \(8~k\Omega\) resistor.
Example
Find \(I_x\).
Solution
The current flowing into the top node is \(4~mA\). The current flowing out of the top node is \(4 I_x\).
Using KCL, we can then find \(I_x\).