BEE DIRECT CURRENT Presentation.ppt for students
- 1. D.C. Circuits BASIC TERMINOLOGY ELECTRIC CIRCUIT ELECTRIC NETWORK CURRENT VOLTAGE POWER
- 2. An electric circuit contains a closed path for providing a flow of electrons from a voltage source or current source. The elements present in an electric circuit will be in series connection, parallel connection, or in any combination of series and parallel connections. 1. Electric Circuit
- 3. An electric network need not contain a closed path for providing a flow of electrons from a voltage source or current source. Hence, we can conclude that "all electric circuits are electric networks" but the converse need not be true. 2. Electric Network
- 4. The current "I" flowing through a conductor is nothing but the time rate of flow of charge. Mathematically, it can be written as I= 𝒅𝑸 𝒅𝑻 Where, Q is the charge and its unit is Coloumb. t is the time and its unit is second. In general, Electron current flows from negative terminal of source to positive terminal, whereas, Conventional current flows from positive terminal of source to negative terminal. 3. Current
- 5. Voltage The voltage "V" is nothing but an electromotive force that causes the charge (electrons) to flow. Mathematically, it can be written as V= 𝑑𝑊 𝑑𝑄 Where, W is the potential energy and its unit is Joule. Q is the charge and its unit is Coloumb. As an analogy, Voltage can be thought of as the pressure of water that causes the water to flow through a pipe. It is measured in terms of Volt. 4.Voltage
- 6. The power "P" is nothing but the time rate of flow of electrical energy. Mathematically, it can be written as P= 𝑑𝑊 𝑑𝑡 Where, W is the electrical energy and it is measured in terms of Joule. t is the time and it is measured in seconds. We can re-write the above equation a P= 𝑑𝑊 𝑑𝑡 = 𝑑𝑊 𝑑𝑄 * 𝑑𝑄 𝑑𝑡 = V*I Therefore, power is nothing but the product of voltage V and current I. Its unit is Watt. 5. Power
- 8. Kirchhoff's Current Law Kirchhoff’s Current Law (KCL) states that the algebraic sum of currents leaving (or entering) a node is equal to zero. A Node is a point where two or more circuit elements are connected to it. If only two circuit elements are connected to a node, then it is said to be simple node. If three or more circuit elements are connected to a node, then it is said to be Principal Node. Mathematically, KCL can be represented as Where, 𝐼𝑚is the 𝑚𝑡ℎ branch current leaving the node. M is the number of branches that are connected to a node. The above statement of KCL can also be expressed as "the algebraic sum of currents entering a node is equal to the algebraic sum of currents leaving a node". Let us verify this statement through the following example.
- 9. Example: Write KCL equation at node P of the following figure. In the above figure, the branch currents I1, I2 and I3 are entering at node P. So, consider negative signs for these three currents. In the above figure, the branch currents I4 and I5 are leaving from node P. So, consider positive signs for these two currents.
- 10. The KCL equation at node P will be In the above equation, the left-hand side represents the sum of entering currents, whereas the right-hand side represents the sum of leaving currents. In this tutorial, we will consider positive sign when the current leaves a node and negative sign when it enters a node. Similarly, you can consider negative sign when the current leaves a node and positive sign when it enters a node. In both cases, the result will be same. Note − KCL is independent of the nature of network elements that are connected to a node.
- 11. Kirchhoff’s Voltage Law Kirchhoff’s Voltage Law (KVL) states that the algebraic sum of voltages around a loop or mesh is equal to zero. A Loop is a path that terminates at the same node where it started from. In contrast, a Mesh is a loop that doesn’t contain any other loops inside it. Mathematically, KVL can be represented as Where, 𝑽𝒏 is the nth element’s voltage in a loop (mesh). N is the number of network elements in the loop (mesh).
- 12. The above statement of KVL can also be expressed as "the algebraic sum of voltage sources is equal to the algebraic sum of voltage drops that are present in a loop." Let us verify this statement with the help of the following example. Example: Write KVL equation around the loop of the following circuit. The above circuit diagram consists of a voltage source, VS in series with two resistors R1 and R2. The voltage drops across the resistors R1 and R2 are V1 and V2 respectively. Apply KVL around the loop.
- 13. In the above equation, the left-hand side term represents single voltage source VS. Whereas, the right-hand side represents the sum of voltage drops. In this example, we considered only one voltage source. That’s why the left-hand side contains only one term. If we consider multiple voltage sources, then the left side contains sum of voltage sources. In this tutorial, we consider the sign of each element’s voltage as the polarity of the second terminal that is present while travelling around the loop. Similarly, you can consider the sign of each voltage as the polarity of the first terminal that is present while travelling around the loop. In both cases, the result will be same. Note − KVL is independent of the nature of network elements that are present in a loop.
- 14. NORTON’S THEOREM Statement: A linear two-terminal circuit can be replaced by an equivalent circuit consisting of a current source 𝐼𝑁in parallel with a resistor 𝑅𝑁 , where 𝐼𝑁is the short-circuit current through the terminals and 𝑅𝑁 is the input or equivalent resistance at the terminals when the independent sources are turned off. Why are we using Norton’s Theorem? • Simplifies the network in terms of currents instead of voltages. •It reduces a network to a simple parallel circuit with a current source and a resistor.
- 16. Steps to determine Norton’s equivalent Resistance (𝑅𝑁) and Current (𝐼𝑁 ): Calculate RN in the same way as 𝑅𝑇ℎ. • Using source transformation, the Thevenin and Norton resistances are equal i.e. 𝑅𝑁 = 𝑅𝑇ℎ. • To find the Norton current 𝐼𝑁 , we determine the short-circuit current flowing from terminal a to b. • This short-circuit current is the Norton equivalent current 𝐼𝑁.
- 17. Close relationship between Norton’s and Thevenin’s theorems:
- 18. Since 𝑉𝑇ℎ, 𝐼𝑁 , and 𝑅𝑇ℎ 𝑁 are related, to determine the Thevenin or Norton equivalent circuit we find: • The open-circuit voltage 𝑣𝑜𝑐 across terminals a and b (= 𝑉𝑇ℎ) • The short-circuit current 𝑖𝑠𝑐 at terminals a and b (= 𝐼𝑁 ) • The equivalent input resistance 𝑅𝑖𝑛 at terminals a and b when all independent sources are turned off (= 𝑅𝑇ℎ 𝑁 )
- 19. Example of Norton Theorem Case 1: Without dependent source
- 20. Example of Norton Theorem Case 2: With dependent source
- 21. Step 1: Compute 𝑅𝑁. Set the independent sources equal to zero and connect a voltage source 𝑣𝑜= 1V to the terminals. We ignore the 4-Ω resistor because it is short-circuited. Hence, 𝑖𝑥= 0. Also due to the short circuit, the 5-Ω resistor, the voltage source, and the dependent current source are all in parallel. At node a, 𝑖0= 1 5 = 0.2A
- 22. Step 2: Compute 𝐼𝑁 Short-circuit terminals a and b and find the current 𝑖𝑠𝑐, as indicated in the figure. Note from this figure that the 4Ω resistor, the 10V voltage source, the 5Ω resistor, and the dependent current source are all in parallel.
- 24. Thank You