![]() This node, by definition, cannot have a voltage drop. Next, we can eliminate the zero voltage term on the left to simplify this equation:Īs an aside, it should be relatively easy to see that we could have skipped measuring that 0 V section of the loop since it is a single electrical node. Having completed our trace of the left loop, we can add these voltages together with a sum of zero as required by KVL: Measure the voltage across resistor R 2.įigure 8. Measure the voltage across the bottom wire segment.įigure 7. Measure the voltage across battery B1.įigure 6. The sequence of voltage measurements is shown below in Figures 5 through 8.įigure 5. We must tally voltage drops in a loop of the circuit as though we measure with a real voltmeter.įirst, let’s trace the left loop of this circuit first, starting from the upper-left corner and moving counter-clockwise (the choice of starting points and directions is arbitrary). Kirchhoff’s voltage law tells us that the algebraic sum of all voltages in a loop must equal zero. Step 2: Applying Kirchhoff’s Voltage Law (KVL) to the Left Circuit Loop The magnitude of the solution, however, will still be correct. A negative current and resistance simply mean the current flows opposite to the direction of our initial guess. As stated earlier, if your assumption happens to be incorrect, it will be apparent once the equations have been solved. The important thing to remember here is to base all your resistor polarities and subsequent calculations on the directions of currents initially assumed. In some cases, we may discover that current will be forced back through a battery, causing this effect (an example of reverse current flow into a battery is when charging a rechargeable battery). Keep in mind that it is okay if the polarity of a resistor’s voltage drop doesn’t match with the polarity of the nearest battery, so long as the resistor voltage polarity is correctly based on the assumed direction of the current through it. Since batteries are sources, the voltage is higher on the side the current exits-just the opposite of the resistive loads. The battery polarities remain as they were according to their symbology, with the short-end negative and the long-end positive. The voltage will be higher on the side the current enters the resistor and lower where it exits. The polarity or the resistor voltages is consistent with a load that is dropping voltage. Label the voltage drops across the resistors. The polarity is positive where the current enters the resistor and negative where it exits the resistor, as shown in Figure 4.įigure 4. Next, we’ll use KVL around the loops in the circuit to develop a set of equations that will allow us to solve for unknown equations.īefore applying KVL, we will label all of the voltage drop polarities across resistors according to the assumed directions of the currents. This situation gives us the following KCL equation:Īpplying Kirchhoff’s Voltage Law Around the Circuit Loop Thus, we can relate these three currents (I 1, I 2, and I 3) to each other in a single equation.įor the sake of convention, let’s denote any current entering the node as a positive and any current exiting the node as negative. Kirchhoff’s current law tells us that the algebraic sum of currents entering and exiting a node must equal zero. Fortunately, if it turns out that any of our guesses were wrong, we will know when we mathematically solve for the currents-any “wrong” current directions will show up as negative numbers in our solution.Īpplying Kirchhoff’s Current Law (KCL) at the Selected Node Keep in mind that these directions of current are speculative at this point. Define all the unknown currents at the selected node. Select a circuit node at which you will define the unknown currents.Īt this node, we will guess which directions the three wire’s currents take, labeling the three currents as I 1, I 2, and I 3, respectively, as illustrated in Figure 3.įigure 3. We’ll choose the node joining the right of R 1, the top of R 2, and the left of R 3, as shown in Figure 2.įigure 2. The first step is to choose a node (junction of wires) in the circuit to use as a point of reference for our unknown currents. Circuit for explaining the branch current method. To begin with, let’s use the circuit in Figure 1 to explain the application of the branch current method.įigure 1. ![]() ![]() Selecting a Circuit Node and Branch Current Assignments Once we have one equation for every unknown current, we can solve the simultaneous equations and determine all currents and, therefore, all voltage drops in the network. In this method, we assume the directions of the currents in the circuit and then write equations describing their relationships to each other through Kirchhoff’s current law (KCL), Kirchhoff’s voltage law (KVL), and Ohm’s law. The most straightforward DC network analysis technique is the branch current method.
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