Series and Parallel Circuits Kirchoff ’s Voltage and Current Laws Circuits 1 Fall 2005 Harding University Jonathan White Outline Node definition KCL KVL The sum of voltages around a closed loop is 0. Series circuits The current entering a node is equal to the current leaving a node. Resistors in series add Req is always greater than R1 and R2 Voltage Dividers Parallel circuits Resistors in parallel follow the equation Req = (R1*R2)/(R1+R2). Req is always less than R1 and R2 Nodes A node is where 2 or more elements meet. For now, and element can be a resistor, a voltage source, or a current source. Each point in the node must be electrically the same. Exp: Kirchoff ’s Current Law A fundamental law of nature, like the Law of Conservation of Mass. KCL is the conservation of charge – charge can neither be created or destroyed. KCL definition: The sum of all currents entering a node is equal to the sum of all currents leaving the node. KCL holds for every node in a network and it works at every point in time. KCL Write equations for the current in each of the nodes in the circuit below: Kirchoff ’s Voltage Law A fundamental law of nature, like the Law of Conservation of Energy. KVL is the conservation of electrical energy – electrical energy can neither be created or destroyed, only transferred. KVL – 2 1. 2. 3. 4. 5. 6. As the charge moves from the top of the battery to the top of Element #1 (along the wire shown in purple), how much energy does the charge lose? As the charge moves from the top of Element #1 through Element #1 to the bottom of element #1, how much energy does the charge lose? As the charge moves from the bottom of Element #1 to the top of Element #2, how much energy does the charge lose? As the charge moves from the top of Element #2 through Element #2 to the bottom of element #2, how much energy does the charge lose? As the charge moves from the bottom of Element #2 to the bottom of the battery, how much energy does the charge lose? As the charge moves from the bottom of the battery through the battery to the top of the battery, how much energy does the charge lose? KVL - 3 What is Vb equal to? KVL definition: the sum of voltages around a closed loop is 0. KVL - 4 Write all the KVL equations for the circuit below: Series Resistance 2 devices are said to be in series when the same current physically flows through both. Current flows into one element, through the element, out of the element into the other element, through the second element and out of the second element. No part of the current that flows through one resistor "escapes" and none is added. You see series resistance everyday Series Resistance - 2 Consider the simplest series resistance: What is Vs ? The equivalent resistance for resistors in series is always the sum of the individual resistors. Voltage Dividers Used as volume controls in electronic devices Provides a continuous sound spectrum, i.e., not digital. Used in RC combinations to filter out input noise in devices such as tachometers and … A voltage divider looks like this: Voltage Dividers - 2 How much current flows through Ra and Rb ? Use Ohm’s Law. What is Vout ? As Rb goes to 0, what’s the value of Vout ? Rb is then physically like what? As Rb goes to ∞, what’s the value of Vout ? Rb is then physically like what? Parallel Resistors 2 resistors are in parallel if the same physical voltage appears across each resistor. Each resistor provides its own path for the flow of current. If the resistors have different resistance values, they will carry different amounts of current, each in accordance with Ohm's Law. Parallel Resistors - 2 Consider the simplest parallel resistance to the right. What is Ip? In parallel resistors, the equivalent resistance is always lower than either of the resistors.