gen-define-kirchhoff-s-voltage-law-and-give-one-short-worked-exa-b194

Define Kirchhoff's voltage law and give one short worked example.

# Kirchhoff's Voltage Law (KVL) ## Definition **Kirchhoff's Voltage Law states that the algebraic sum of all voltages around any closed loop in a circuit equals zero.** Mathematically: **ΣV = 0** around any closed loop This reflects the conservation of energy—the energy gained per unit charge must equal the energy lost as you travel around a complete loop. ## Sign Convention - Voltage **rises** (- to +) are **positive** - Voltage **drops** (+ to -) are **negative** ## Worked Example Consider a simple series circuit with: - A 12V battery - A 5Ω resistor - A 3Ω resistor **Find the current flowing through the circuit.** **Solution:** Starting at the negative terminal and going clockwise around the loop: 1. Across the battery: **+12V** (voltage rise) 2. Across the 5Ω resistor: **-5I** (voltage drop) 3. Across the 3Ω resistor: **-3I** (voltage drop) Applying KVL: $$+12 - 5I - 3I = 0$$ $$12 - 8I = 0$$ $$I = 1.5 \text{ A}$$ **Answer: The current is 1.5 A**