Electronics: A Guide for Physicists (DRAFT -- in development)

Kirchhoff’s Current Law (KCL), or Junction Law, relies on conservation of charge to say that the rate at which charges enter a junction must be equivalent to the rate at which charges leave the junction

for a scenario as pictured in Figure 2.1.1. The KCL can also be represented mathematically as

where $I_i<0$ for currents leaving a node and $I_i>0$ for currents entering a node.

Another conservation law, the conservation of energy, is ultimately responsible for what we call Kirchhoff’s Voltage Law (KVL), or the Loop Law. If one walks around any loop in a circuit (such as that shown in Figure 2.1.2), the sum of the voltage changes as one moves in a single direction around a complete loop must add up to zero, or

When using the KVL equation, voltages rise as one crosses a voltage source from the negative terminal to positive terminal and voltages fall in the opposite direction. Additionally, voltages fall across a resistor in the direction of current and rise in the opposite direction.

The last rule we’ll introduce here is Ohm’s Law. For the situation shown in Figure 2.1.3, the magnitude of the voltage change across a resistor is dependent on the resistance and the magnitude of current in the resistor according to

where $\mathrm{\Delta }V=V_A-V_B\text{.}$ A note on signs: When using Ohm’s law, $\mathrm{\Delta }V$ and $I$ actually represent $\left|\mathrm{\Delta }V\right|$ and $\left|I\right|\text{.}$ It is conventional to use Ohm’s law to relate magnitudes of $\mathrm{\Delta }V$ to $I\text{.}$ The signs on each variable are linked by the fact that current is directed from high to low voltage. So, if current is in the direction indicated in Figure 2.1.3, then $V_A>V_B\text{.}$