Kirchhoff's Laws
Kirchhoff's Laws are two essential rules in electrical engineering that deal with the conservation of current and energy in electrical circuits. These laws are known as:
- Kirchhoff’s Current Law (KCL)
- Kirchhoff’s Voltage Law (KVL)
Kirchhoff’s Current Law (KCL)
Kirchhoff’s Current Law states that the total current entering a junction (or node) in an electrical circuit must equal the total current leaving the junction.
In formula terms: ∑ Iin = ∑ Iout
This law is based on the conservation of electric charge — no charge is lost at a node.
Example of KCL:
Suppose three currents meet at a node: 5 A enters, 2 A leaves, and one unknown current leaves. What is the unknown current?
5 A = 2 A + I
I = 5 A - 2 A = 3 A
Answer: The unknown current leaving the node is 3 amperes.
Kirchhoff’s Voltage Law (KVL)
Kirchhoff’s Voltage Law states that the sum of all electrical potential differences (voltages) around any closed loop in a circuit must be zero.
In formula terms: ∑ V = 0
This law is based on the conservation of energy — the total energy gained per loop is equal to the total energy lost.
Example of KVL:
Suppose you have a loop with a 12 V battery and two resistors causing voltage drops of 7 V and 5 V. Does KVL hold?
12 V - 7 V - 5 V = 0 V
Answer: Yes, Kirchhoff’s Voltage Law is satisfied.
Summary:
- KCL: Currents into a node = Currents out of a node
- KVL: The sum of voltages around a loop = 0
Kirchhoff's Law Practical Examples
Example 1: Kirchhoff’s Current Law (KCL) - Finding Unknown Current
At a junction, three currents are involved: 8 A enters, 3 A leaves, and another current (I) leaves. What is the value of the unknown current?
Formula: ∑ Iin = ∑ Iout
Substitute the values: 8 A = 3 A + I
Solve: I = 8 A - 3 A = 5 A
Answer: The unknown current is 5 amperes.
Example 2: Kirchhoff’s Voltage Law (KVL) - Checking a Loop
In a closed loop, there is a 9 V battery and two resistors causing voltage drops of 4 V and 5 V respectively. Verify if KVL holds.
Formula: ∑ V = 0
Substitute the values: 9 V - 4 V - 5 V = 0 V
Answer: Yes, the voltages balance, and Kirchhoff’s Voltage Law is satisfied.
Example 3: Kirchhoff’s Voltage Law (KVL) - Finding an Unknown Voltage
In a loop, a 15 V battery is connected across two components. One causes a 6 V drop, and the other causes an unknown drop (Vx). Find the value of Vx.
Formula: 15 V - 6 V - Vx = 0
Rearranging: Vx = 15 V - 6 V = 9 V
Answer: The unknown voltage drop is 9 volts.