recall Kirchhoff’s second law and understand that it is a consequence of conservation of energy

Kirchhoff’s Laws

⚡️ Kirchhoff’s Laws are the rules that let us analyse any electrical circuit, no matter how complex. They are based on two fundamental ideas: conservation of charge and conservation of energy. In this lesson we’ll focus on the second law – the Voltage Law – and see why it is simply a statement of energy conservation.

Kirchhoff’s Second Law (Voltage Law)

🔋 Imagine a circular water‑pipe system. If you start at any point and go around the loop, the total change in water pressure must be zero – you can’t magically create or destroy pressure. In electrical terms, if you start at one point in a closed loop and add up all the voltage rises (positive) and drops (negative), the sum must be zero: $$\sum_{\text{loop}} V = 0$$ For a simple loop with two batteries and one resistor it looks like: $$V_{\text{bat1}} + V_{\text{bat2}} - I R = 0$$ where $I$ is the current and $R$ the resistance.

Why It Follows from Conservation of Energy

💡 Energy conservation says that energy put into a system must equal energy taken out. In a loop, the energy supplied by batteries (voltage × current) is exactly the energy lost as heat in resistors (I²R) or stored in capacitors/inductors. Mathematically, the work done by each element around the loop adds to zero: $$\sum_{\text{elements}} (V \cdot I) = 0$$ Since $I$ is the same in a series loop, we can factor it out and get the familiar voltage sum above.

Example Circuit

⚡️ Check your work: Add the voltages in the order you traverse the loop. If you get zero, you’ve applied Kirchhoff’s second law correctly.

Exam Tips

1️⃣ Label every element (battery, resistor, etc.) and mark the direction of current. 2️⃣ Choose a loop that includes all unknowns. 3️⃣ Write the sum of voltages with correct signs: + for rises, – for drops. 4️⃣ Check units – everything should be in volts. 5️⃣ Remember the energy view: the sum of energy supplied equals the sum of energy dissipated. 6️⃣ Practice with different loop directions – the result will always be zero, but the algebra changes sign.

🎓 Remember: Kirchhoff’s second law is just the electrical version of “you can’t get free energy.” If you can’t balance the voltages, you’re missing something in your circuit diagram. Keep practicing and the loop equations will become second nature!