Basics of Electric circuit theory
- 1. 1 Basics of Circuit Circuit Theory Prof. Mohsin A Mulla Asst. Professor, EE SITCOE, Yadrav.
- 2. 2 Basic Laws 2.1 Ohm’s Law. 2.2 Nodes, Branches, and Loops. 2.3 Kirchhoff’s Laws. 2.4 Series Resistors and Voltage Division. 2.5 Parallel Resistors and Current Division. 2.6 Wye-Delta Transformations.
- 3. 3 2.1 Ohms Law (1) • Ohm’s law states that the voltage across a resistor is directly proportional to the current I flowing through the resistor. • Mathematical expression for Ohm’s Law is as follows: • Two extreme possible values of R: 0 (zero) and (infinite) are related with two basic circuit concepts: short circuit and open circuit. iRv
- 4. 4 2.1 Ohms Law (2) • Conductance is the ability of an element to conduct electric current; it is the reciprocal of resistance R and is measured in mhos or siemens. • The power dissipated by a resistor: v i R G 1 R v Rivip 2 2
- 5. 5 2.2 Nodes, Branches and Loops (1) • A branch represents a single element such as a voltage source or a resistor. • A node is the point of connection between two or more branches. • A loop is any closed path in a circuit. • A network with b branches, n nodes, and l independent loops will satisfy the fundamental theorem of network topology: 1 nlb
- 6. 6 2.2 Nodes, Branches and Loops (2) Example 1 How many branches, nodes and loops are there? Original circuit Equivalent circuit
- 7. 7 2.2 Nodes, Branches and Loops (3) Example 2 How many branches, nodes and loops are there? Should we consider it as one branch or two branches?
- 8. 8 2.3 Kirchhoff’s Laws (1) • Kirchhoff’s current law (KCL) states that the algebraic sum of currents entering a node (or a closed boundary) is zero. 0 1 N n niMathematically,
- 9. 9 2.3 Kirchhoff’s Laws (2) Example 4 • Determine the current I for the circuit shown in the figure below. I + 4-(-3)-2 = 0 I = -5A This indicates that the actual current for I is flowing in the opposite direction.We can consider the whole enclosed area as one “node”.
- 10. 10 2.3 Kirchhoff’s Laws (3) • Kirchhoff’s voltage law (KVL) states that the algebraic sum of all voltages around a closed path (or loop) is zero. Mathematically, 0 1 M m nv
- 11. 11 2.3 Kirchhoff’s Laws (4) Example 5 • Applying the KVL equation for the circuit of the figure below. va-v1-vb-v2-v3 = 0 V1 = IR1 v2 = IR2 v3 = IR3 va-vb = I(R1 + R2 + R3) 321 RRR vv I ba
- 12. 12 2.4 Series Resistors and Voltage Division (1) • Series: Two or more elements are in series if they are cascaded or connected sequentially and consequently carry the same current. • The equivalent resistance of any number of resistors connected in a series is the sum of the individual resistances. • The voltage divider can be expressed as N n nNeq RRRRR 1 21 v RRR R v N n n 21
- 13. 13 Example 3 10V and 5W are in series 2.4 Series Resistors and Voltage Division (1)
- 14. 14 2.5 Parallel Resistors and Current Division (1) • Parallel: Two or more elements are in parallel if they are connected to the same two nodes and consequently have the same voltage across them. • The equivalent resistance of a circuit with N resistors in parallel is: • The total current i is shared by the resistors in inverse proportion to their resistances. The current divider can be expressed as: Neq RRRR 1111 21 n eq n n R iR R v i
- 15. 15 Example 4 2W, 3W and 2A are in parallel 2.5 Parallel Resistors and Current Division (1)