CIRCUIT THEORY CHAPTER 2 BASIC LAWS CONTINUE BASIC

CIRCUIT THEORY CHAPTER 2 BASIC LAWS (CONTINUE)

BASIC LAWS CHAPTER 2 2. 3 Kirchhoff’s Laws. 2. 4 Series Resistors and Voltage Division. 2. 5 Parallel Resistors and Current Division. 2. 6 Wye-Delta Transformations.

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. Mathematically,

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 ÞI = -5 A We can consider the whole enclosed area as one “node”. This indicates that the actual current for I is flowing in the opposite direction.

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,

2. 3 KIRCHHOFF’S LAWS Example Applying the KVL equation for the circuit of the figure below. va-v 1 -vb-v 2 -v 3 = 0 V 1 = IR 1 v 2 = IR 2 v 3 = IR 3 Þ va-vb = I(R 1 + R 2 + R 3)

Example For the circuit in Fig. , find voltages v 1 and v 2. Solution To find v 1 and v 2, we apply Ohm’s law and Kirchhoff’s voltage law. Assume that current i flows through the loop as shown in Fig. (b). From Ohm’s law, v 1 = 2 i, v 2 = − 3 i Applying KVL around the loop gives − 20 + v 1 − v 2 = 0 Substituting Eq. (2. 5. 1) into Eq. (2. 5. 2), we obtain − 20 + 2 i + 3 i =0 or 5 i = 20 ⇒ i = 4 A Substituting i in Eq. (2. 5. 1) finally gives v 1 = 8 V, v 2 = − 12 V

2. 4 SERIES RESISTORS AND VOLTAGE DIVISION 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

2. 4 SERIES RESISTORS AND VOLTAGE DIVISION Example 10 V and 5 W are in series

2. 5 Parallel Resistors and Current Division 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 in parallel is: N resistors The total current i is shared by the resistors in inverse proportion to their resistances. The current divider can be expressed as:

2. 5 Parallel Resistors and Current Division Example 2 W, 3 W and 2 A are in parallel

2. 6 WYE-DELTA TRANSFORMATIONS Delta -> Star -> Delta