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Transcript
NASA-Threads Electricity and Magnetism Lesson 14: KVL Lesson 14: Kirchhoff’s Voltage Law (KVL) Get together in groups of 2 or 4 Arrange your sources and loads in various configurations For each configuration, measure the voltage across each source and each load Prove Kirchhoff’s Voltage Law (KVL) by showing that the sum of the voltages around any circuit is zero Here are some of the possible configurations of sources and loads (the batteries depicted below should actually be battery packs with 1 – 4 batteries installed): NASA-Threads Electricity and Magnetism 3 V Source Lesson 14: KVL + VLoad - Start loop here, go around the loop and return to this point Experiment with some (or all) of the possible configurations for 2 or 4 battery packs. For each configuration, record the voltage across each source (battery pack) and each load (light bulb). Write a paragraph explaining their observations about each configuration. Consider the voltage across each source as a positive value and the voltage across each load as a negative value, with these sign assignments, they should be able to show that the sum of the voltages around each of their configurations sums to zero volts. Kirchhoff’s Voltage Law Due to the conservation of energy, the sum of the voltage sources (taken as positive values) and the voltage loads (taken as negative values) around any loop in an electrical circuit sums to zero. When working KVL problems, we want to consider voltage sources to be positive and voltage loads to be negative. With that sign convention, the sum of the voltages around any loop in a circuit sill be zero. With that in mind, consider the circuit shown to the right. If we start in the lower left hand corner, as indicated, and proceed around the loop in a clockwise direction, we will end up back in the lower left hand corner and we will have encountered one voltage source and one voltage load along the way. NASA-Threads Electricity and Magnetism Lesson 14: KVL The source and the load both have polarity markings on them indicating which side of the element has the higher voltage. As we move around the loop, we can show sources as positive and loads as negative if we assign each element the polarity we find as we leave that element. In this case, as we start in the lower left hand corner and proceed up, we encounter the 3 V voltage source first. We find the negative polarity sign first as we enter this element and we find the positive sign as we continue upward and leave this element. So we will assign this voltage a positive sign value as that is the polarity sign we find as we leave this element. As we continue around the loop we encounter the load as we move in a downward direction. We find the positive polarity sign first as we enter this element and the negative polarity sign as we leave this element, so we will assign this voltage a negative sign. Applying Kirchhoff’s Voltage Law, the sum of these voltages with these assigned sign values must be zero. +3𝑉 + (−𝑉𝐿𝑜𝑎𝑑) = 0 As we solve this equation, we find that the value of VLoad equals +3V. +3𝑉 − 𝑉𝐿𝑜𝑎𝑑 = 0 +3𝑉 = 𝑉𝐿𝑜𝑎𝑑 To summarize, whenever we use Kirchhoff’s Voltage Law to sum the voltages around a loop, we must always assign a sign value to each of the voltages. As we proceed around the loop and encounter the voltage elements, we will find a polarity sign as we enter that element and another polarity sign as we leave that element. We assign the sign value we find as we leave that element to the voltage for that element and use that sign value in the equation we form using Kirchhoff’s Voltage Law.