Ohm's Law and Kirchhoff's Laws
Ohm's Law
Ohm's Law is a fundamental principle in electrical engineering that relates voltage (V), current (I), and resistance (R) in an electrical circuit. The law is expressed mathematically as:
V = I * R
Where:
- V is the voltage across the conductor, measured in volts (V).
- I is the current flowing through the conductor, measured in amperes (A).
- R is the resistance of the conductor, measured in ohms (Ω).
Example: If a resistor has a resistance of 10 ohms and a current of 2 amperes is flowing through it, the voltage across the resistor can be calculated as:
V = I * R = 2 A * 10 Ω = 20 V
Kirchhoff's Laws
Kirchhoff's Laws are two fundamental laws in circuit analysis that help in understanding the behavior of current and voltage in a circuit. These laws are:
Kirchhoff's Current Law (KCL)
Kirchhoff's Current Law states that the sum of currents entering a node (or a junction) in a circuit is equal to the sum of currents leaving that node. Mathematically, it can be expressed as:
ΣIin = ΣIout
Example: Consider a junction where three wires meet. If currents I1 = 3 A, I2 = 5 A, and I3 = -2 A are entering or leaving the junction, the sum of currents is:
I1 + I2 + I3 = 3 A + 5 A - 2 A = 6 A
This means that the total current entering the junction is equal to the total current leaving the junction.
Kirchhoff's Voltage Law (KVL)
Kirchhoff's Voltage Law states that the sum of voltages around any closed loop in a circuit is equal to zero. Mathematically, it can be expressed as:
ΣV = 0
Example: Consider a simple circuit with a battery of 12 V and two resistors in series, R1 = 4 Ω and R2 = 8 Ω. The voltage drops across the resistors can be calculated using Ohm's Law:
V1 = I * R1 and V2 = I * R2
Assuming a current I = 1 A, the voltage drops are:
V1 = 1 A * 4 Ω = 4 V
V2 = 1 A * 8 Ω = 8 V
Applying KVL around the loop:
12 V - V1 - V2 = 12 V - 4 V - 8 V = 0
This confirms that the sum of voltages around the loop is zero.