use the formula for the combined resistance of two or more resistors in parallel

Kirchhoff’s Laws

⚡️ Kirchhoff’s Current Law (KCL) – The total current entering a junction equals the total current leaving it. Think of water flowing into a forked pipe: the amount of water that comes in must equal the amount that goes out.

🔌 Kirchhoff’s Voltage Law (KVL) – The sum of all voltage drops around any closed loop equals the sum of the voltage rises. Imagine walking around a circular track: the total uphill climb must equal the total downhill descent.

Combined Resistance of Resistors in Parallel

When resistors are connected side‑by‑side (parallel), the overall resistance is lower than any single resistor. The formula is:

Exam Tip: Always write the reciprocal of the equivalent resistance first, then invert at the end. This helps avoid sign errors.

Example: Two resistors, 10 Ω and 20 Ω, in parallel.

1. Write the reciprocal: $\displaystyle \frac{1}{R_{\text{eq}}} = \frac{1}{10} + \frac{1}{20} = 0.1 + 0.05 = 0.15$.
2. Invert to find $R_{\text{eq}}$: $\displaystyle R_{\text{eq}} = \frac{1}{0.15} \approx 6.67\ \Omega$.

🎓 Quick Check: If you add more resistors in parallel, the equivalent resistance will keep decreasing, approaching zero as the number of resistors grows.

Applying Kirchhoff’s Laws to Parallel Circuits

1️⃣ Use KCL to find the total current entering the junction. 2️⃣ Use KVL around each loop to relate voltage drops and supply voltage. 3️⃣ Use the parallel resistance formula to simplify the circuit before solving for unknowns.

Exam Tip: Sketch the circuit, label all currents and voltages, and then apply KCL and KVL systematically. This reduces confusion and ensures you don’t miss any equations.