4.3 KVL Example Circuits

## Introduction After learning the idea behind KVL, the next step is seeing it applied in real circuits. Many technicians understand the rule in theory, but the skill shows up when you can walk through loops confidently, handle sign conventions, and solve for unknown voltages. Hands-on examples build that confidence. These example circuits show how KVL works in simple loops you will see in benches, vehicles, control cabinets, and low-voltage power systems. Each case shows the thinking process so you can apply the same steps in your own troubleshooting. ## Key Concept Kirchhoff’s Voltage Law states that the sum of all voltages around a closed loop must equal zero: $\sum V = 0.$ To apply KVL in practice, remember the basic sign rules: - Moving from the negative terminal to the positive terminal of a source is a **voltage rise**. - Moving through a resistor in the direction of current flow is a **voltage drop**. - Voltage drops are negative, rises are positive. > [!info] When to Use KVL > Use KVL whenever you need to check total loop voltage, verify a component drop, locate unexpected resistance, or identify wiring errors. ## How It Works Below are several example circuits walked through step by step. ### Example 1: Simple Series Loop A 12 V source feeds two resistors in series: 3 Ω and 9 Ω. Find the voltage drop across each resistor. 1. **Find total resistance:** $R_T = 3\ \Omega + 9\ \Omega = 12\ \Omega.$ 2. **Find total current:** $I = \frac{12\ V}{12\ \Omega} = 1\ A.$ 3. **Apply Ohm’s Law to each resistor:** - Drop across 3 Ω resistor: $V_1 = 1\ A \times 3\ \Omega = 3\ V.$ - Drop across 9 Ω resistor: $V_2 = 1\ A \times 9\ \Omega = 9\ V.$ 4. **Apply KVL:** $+12\ V - 3\ V - 9\ V = 0.$ This confirms the math and the loop behavior. ### Example 2: Loop With a Switch Contact A 24 V control loop includes a relay coil and a normally closed stop switch. The coil is rated for 18 V at the operating current. The coil is not energizing fully. You measure the following: - Voltage across source: 24 V - Voltage drop across coil: 17 V - Unknown drop across stop switch Applying KVL: $+24\ V - 17\ V - V_{switch} = 0.$ Solve for the switch drop: $V_{switch} = 7\ V.$ A stop switch in good condition should drop almost zero volts. A 7 V drop clearly indicates a failing or contaminated contact. KVL makes the fault easy to spot. ### Example 3: Mixed Load Series Circuit A bench test uses a 10 V supply feeding a resistor and a small LED indicator in series. Measured data: - LED forward drop: 2 V - Total loop current: 20 mA Find the resistor value. Apply KVL: $+10\ V - 2\ V - V_R = 0.$ So the resistor drop is: $V_R = 8\ V.$ Now solve for resistance: $R = \frac{8\ V}{0.02\ A} = 400\ \Omega.$ This example shows how KVL and Ohm’s law work together to confirm component choices. ### Example 4: Loop With a Faulty Connection A technician measures a 48 V DC circuit feeding a solenoid and sees poor pulling strength. Measurements show: - Source: 48 V - Drop across solenoid: 42 V - Remaining drop: 6 V (unaccounted) KVL: $+48\ V - 42\ V - V_{unknown} = 0.$ $V_{unknown} = 6\ V.$ That 6 V drop is happening somewhere in the wiring, likely at a loose terminal or corroded splice. Once again, KVL points directly to the fault without guesswork. > [!tip] Field Note > When a device receives less voltage than expected, always check wiring and mechanical connections. Most unexpected drops come from copper oxidation or loose screw terminals. ### Example 5: Multi-Element Loop With Measurement Check A device uses a 15 V supply feeding three resistors in series: 100 Ω, 220 Ω, and 680 Ω. 1. **Find total resistance:** $R_T = 100 + 220 + 680 = 1000\ \Omega.$ 2. **Find loop current:** $I = \frac{15\ V}{1000\ \Omega} = 0.015\ A.$ 3. **Find each drop:** - $V_1 = 0.015 \times 100 = 1.5\ V.$ - $V_2 = 0.015 \times 220 = 3.3\ V.$ - $V_3 = 0.015 \times 680 = 10.2\ V.$ 4. **Apply KVL:** $+15\ V - 1.5\ V - 3.3\ V - 10.2\ V = 0.$ In the field, if your measured drops do not match calculated values, KVL helps you identify which part of the loop is out of tolerance. ## Real-World Application Technicians use KVL constantly when checking control power circuits. For example, if an emergency stop string shows inconsistent behavior, you can measure each contact’s drop and use KVL to confirm which device is causing excessive resistance. KVL also helps when confirming correct polarity or voltage distribution in DC UPS systems, battery banks, or PLC input loops. When learning troubleshooting, techs often jump straight to resistance checks. But KVL-based voltage measurement under load gives much more reliable information. ## Safety Notes Always verify that your test equipment is properly rated for the system. When measuring voltage in a live loop, keep both hands away from grounded surfaces and use your meter probes deliberately. Follow NFPA 70E guidance when panels are open or energized. > [!caution] Meter Safety > Never adjust your meter dial while your probes are connected to live conductors. ## Summary KVL becomes easier when you walk through example circuits. By breaking a loop into rises and drops, you can solve for unknown values and locate unexpected voltage losses. With practice, you will recognize KVL patterns naturally and use them to troubleshoot faster and more accurately. These example loops build your skill before we add more complex applications in upcoming lessons. > [!columns] > >[!info] Previous lesson > ⬅️ [[4.2 Kirchhoff’s Voltage Law (KVL)]] > > >[!info] Next lesson > ➡️ [[4.4 Kirchhoff’s Current Law (KCL)]]