1. Series and Parallel Circuits Kirchoff’s Voltage and Current Laws Circuits 1 Fall 2005 Harding University Jonathan White

2. Outline Node definition Node definition KCL KCL The current entering a node is equal to the current leaving a node. The current entering a node is equal to the current leaving a node. KVL KVL The sum of voltages around a closed loop is 0. The sum of voltages around a closed loop is 0. Series circuits Series circuits Resistors in series add Resistors in series add R eq is always greater than R1 and R2 R eq is always greater than R1 and R2 Voltage Dividers Voltage Dividers Parallel circuits Parallel circuits Resistors in parallel follow the equation R eq = (R 1 *R 2 )/(R 1+ R 2). Resistors in parallel follow the equation R eq = (R 1 *R 2 )/(R 1+ R 2). R eq is always less than R 1 and R 2 R eq is always less than R 1 and R 2

3. Nodes A node is where 2 or more elements meet. A node is where 2 or more elements meet. For now, and element can be a resistor, a voltage source, or a current source. 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. Each point in the node must be electrically the same. Exp: Exp:

4. Kirchoff’s Current Law A fundamental law of nature, like the Law of Conservation of Mass. 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 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 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 holds for every node in a network and it works at every point in time.

5. KCL Write equations for the current in each of the nodes in the circuit below: Write equations for the current in each of the nodes in the circuit below:

6. Kirchoff’s Voltage Law A fundamental law of nature, like the Law of Conservation of Energy. 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 is the conservation of electrical energy – electrical energy can neither be created or destroyed, only transferred.

7. KVL – 2 1. 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? 2. 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? 3. As the charge moves from the bottom of Element #1 to the top of Element #2, how much energy does the charge lose? 4. 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? 5. As the charge moves from the bottom of Element #2 to the bottom of the battery, how much energy does the charge lose? 6. 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?

8. KVL - 3 What is V b equal to? What is V b equal to? KVL definition: the sum of voltages around a closed loop is 0. KVL definition: the sum of voltages around a closed loop is 0.

9. KVL - 4 Write all the KVL equations for the circuit below: Write all the KVL equations for the circuit below:

10. Series Resistance 2 devices are said to be in series when the same current physically flows through both. 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. 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 You see series resistance everyday

11. Series Resistance - 2 Consider the simplest series resistance: Consider the simplest series resistance: What is Vs ? What is Vs ? The equivalent resistance for resistors in series is always the sum of the individual resistors. The equivalent resistance for resistors in series is always the sum of the individual resistors.

12. Voltage Dividers Used as volume controls in electronic devices Used as volume controls in electronic devices Provides a continuous sound spectrum, i.e., not digital. Provides a continuous sound spectrum, i.e., not digital. Used in RC combinations to filter out input noise in devices such as tachometers and … Used in RC combinations to filter out input noise in devices such as tachometers and … A voltage divider looks like this: A voltage divider looks like this:

13. Voltage Dividers - 2 How much current flows through R a and R b ? Use Ohm’s Law. How much current flows through R a and R b ? Use Ohm’s Law. What is V out ? What is V out ? As R b goes to 0, what’s the value of V out ? R b is then physically like what? As R b goes to 0, what’s the value of V out ? R b is then physically like what? As R b goes to ∞, what’s the value of V out ? R b is then physically like what? As R b goes to ∞, what’s the value of V out ? R b is then physically like what?

14. Parallel Resistors 2 resistors are in parallel if the same physical voltage appears across each resistor. 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. 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.

15. Parallel Resistors - 2 Consider the simplest parallel resistance to the right. What is I p ? Consider the simplest parallel resistance to the right. What is I p ? In parallel resistors, the equivalent resistance is always lower than either of the resistors. In parallel resistors, the equivalent resistance is always lower than either of the resistors.