Kirchoff's Laws

Q1: What are Kirchoff's circuit laws?

A1:

1. Kirchoff's Current Law (KCL): The sum of all currents into a node is zero

$\sum\limits_{j=1}^ni_j=0$

2. Kirchoff's Voltage Law (KVL): The sum of all voltages in a loop is zero

$\sum\limits_{j=1}^nv_j=0$

Q2: Why are Kirchoff's circuit laws useful?

A2: You can use Kirchoff's circuit laws to analyze circuits. KCL is used in nodal analysis while KVL is used in mesh analysis. Nodal or mesh analysis may be used to solve circuits.

Q3: Could I get away with just learning nodal analysis? Or just mesh analysis?

A3: You could, but it's handy to be comfortable with both. For example, if you're solving for an unknown voltage, then nodal analysis is more intuitive. On the other hand, if you're solving for an unknown current, then you'd probably turn to mesh analysis.

Q4: Is there another reason (besides convenience) for learning nodal and mesh analysis?

A4: With both methods of analysis, you can check your work. For example, you might first use nodal analysis to solve a circuit. You can then resolve the same circuit using mesh analysis. Disagreement between the results constitutes a failed sanity check (i.e. at least one of your methods of analysis was implemented incorrectly). Agreement between the results means that you passed a sanity check (i.e. your results are not wrong in an obvious way). Note that passing a sanity check does not guarantee correctness of your results. Still, sanity checks are good practice for avoiding blatantly wrong answers.