4.5 KCL Example Circuits

## Introduction Learning KCL in theory is helpful, but real skill comes from walking through example circuits. In the field you often deal with parallel loads, shared conductors, and branching points that feed multiple devices. These example circuits show how to apply KCL step by step so you can calculate branch currents, identify imbalances, and troubleshoot problems quickly. ## Key Concept Kirchhoff’s Current Law (KCL) states: $\sum I_{in} = \sum I_{out}.$ Current reaching a node must equal the current leaving it. There is no storage of current at a junction. If the currents do not add up, something in the circuit is behaving differently than expected. > [!info] Node Reminder > A **node** is any point where two or more conductors join. > A **branch** is any circuit path leaving the node. ## How It Works These examples use Ohm’s Law and KCL together. Each branch current is found with: $I = \frac{V}{R}.$ Once you know the branch currents, the total current into the node must match the total current out. ### Example 1: Two Parallel Resistors A 12 V supply feeds a junction that splits into two resistors: - Branch 1: 4 Ω - Branch 2: 8 Ω Branch currents: - $I_1 = \frac{12}{4} = 3\ A$ - $I_2 = \frac{12}{8} = 1.5\ A$ KCL: - $I_T = I_1 + I_2 = 4.5\ A.$ The supply must provide 4.5 A to the node. ### Example 2: Three Parallel Loads A 24 V DC power supply feeds three devices in parallel: - Solenoid: 60 Ω - Indicator light: 480 Ω - Sensor module: draws 50 mA Find total current. Branch currents: - Solenoid: $I_S = \frac{24}{60} = 0.4\ A$ - Indicator: $I_L = \frac{24}{480} = 0.05\ A$ - Sensor: $I_{sensor} = 0.05\ A$ KCL total: - $I_T = 0.4 + 0.05 + 0.05 = 0.5\ A.$ This confirms the supply must deliver half an amp. ### Example 3: Unbalanced Branch Revealing a Fault A 48 V system splits into two parallel branches: - Branch 1: Normal load draws 1 A - Branch 2: Should draw 1 A, but a clamp reading shows 3 A Total current measured at the source terminal is 4 A. Using KCL: - Expected: $1\ A + 1\ A = 2\ A$ - Actual: $1\ A + 3\ A = 4\ A$ Since Branch 2 is drawing far more than expected, this suggests a short or internal failure. KCL highlights the imbalance immediately. ### Example 4: Using KCL With Measured Data A 10 V supply feeds a node that splits into two resistive branches. A technician measures: - Branch 1 current: 0.12 A - Branch 2 current: 0.08 A KCL says: - $I_T = 0.12 + 0.08 = 0.20\ A$ If the source meter shows 0.16 A, something is off. Either: - Branch currents were measured incorrectly - A high-resistance connection is limiting current - The supply voltage is sagging under load KCL helps identify inconsistencies. > [!note] Field Tip > If KCL numbers do not match, recheck measurement technique first. Clamp placement, meter range, and conductor orientation all affect readings. ### Example 5: Branch Currents After Adding a New Load A technician adds a new indicator lamp to an existing 24 V parallel control branch. Original loads: - Relay coil: 500 Ω - Sensor input: 20 mA New lamp: draws 10 mA Branch currents: - Relay: $\frac{24}{500} = 48\ mA$ - Sensor: 20 mA - Lamp: 10 mA Total: - $I_T = 48\ mA + 20\ mA + 10\ mA = 78\ mA.$ KCL confirms the power supply now carries 78 mA on that branch. This is important for confirming supply sizing and preventing overloads. ### Example 6: Parallel Motor Controls With Shared Feed A control cabinet has two motor starters sharing the same 120 V control feed. Each coil draws: - Starter A: 0.18 A - Starter B: 0.22 A If both contactors energize at the same time: Total: - $I_T = 0.18 + 0.22 = 0.40\ A.$ KCL quickly confirms the expected current through the shared feed conductor. If the measured current is significantly higher, one of the coils may be partially shorted. ## Real-World Application KCL has major value when diagnosing ground faults or leakage currents. If you clamp all conductors entering a device and see a nonzero current, that means current is finding an unintended return path. This is one of the quickest checks for control-circuit grounding problems. KCL also helps you verify multi-load control branches. For example, if a PLC input card is overloaded or behaving inconsistently, checking the branch currents against KCL calculations helps identify which load is drawing more than expected. ## Safety Notes Always use safe current-measurement techniques. Clamp meters are preferred for field work because they do not require opening the circuit. When making inline measurements, de-energize and lock out the system unless the meter and leads are properly rated. Follow NFPA 70E for PPE and boundaries when working inside energized cabinets. > [!warning] Measurement Safety > Clamp only one conductor at a time if you want branch current. Clamping both supply and return together will cancel out the reading. ## Summary KCL gives you a structured way to understand how current divides at nodes. These example circuits show how to calculate branch currents, identify faults, and verify expected behavior. The more you practice, the easier parallel circuits become to troubleshoot. With KVL and KCL covered, you are ready to use both laws together in more complex circuit analysis. > [!columns] > >[!info] Previous lesson > ⬅️ [[4.4 Kirchhoff’s Current Law (KCL)]] > > >[!info] Next lesson > ➡️ [[4.6 Using KVL and KCL Together]]