Kirchoff's Laws are statements about the nature of current and voltage. Unlike Ohm's Law, which describes the behavior of devices in a circuit (impedances), Kirchoff's Laws are rules that explain circuits in general. The laws are as follows:
Kirchoff's Current Law: The current entering any point in a circuit is the same as the current leaving that point in the circuit.
Kirchoff's Voltage Law: The sum of the voltage drops around any loop in a circuit is zero.
These laws come back to fundamental statements of physics. Kirchoff's Current Law (KCL) is, in effect, stating that charge can never be created or destroyed. Kirchoff's Voltage Law (KVL) is a way of stating that the electric field is a conservative force field (just like gravity). Although a physicist may disagree, KCL and KVL should be considered fundamental truths for electrical engineers.
KCL (Green) and KVL (Red) in a Nutshell
Combining KCL, KVL, and Ohm's Law, we can analyze all kinds of circuits to determine their behavior.
Example: For the circuit above, assume all resistors are 1 Ohm and the source voltage Vs is 10 Volts. Determine the value of the current I.
Solution: Begin by using KVL around the circuit loop:
Vs = 10 = Va + Vb
Next, use Ohm's Law to substitute the resistances and currents for the voltages shown:
10 = I + Ia
Now, use KCL to get a second equation for I and Ia. Note that Ia and Ib must be equal since the same voltage is applied across the same resistance in both cases:
I = Ia + Ib = 2 Ia
Substitute for Ia into the KVL and Ohm's Law equation above:
10 = I + I / 2 = 3 I / 2
I = 6.67 A
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