Chapter 2. Resistive circuits 2015. 9. 7.

Contents Ohm’s law Kirchhoff’s laws Series and parallel resistor combinations Y-Δ transformation Circuits with dependent sources

Resistors : microscopic view nucleus electrons Entering resistive material, charges are decelerated, which decrease current flow.

Types of resistors (1), (2), and (3) are high power resistors. (4) and (5) are high-wattage fixed resistors. (6) is a high precision resistor. (7)–(12) are fixed resistors with different power ratings.

1. Ohm’s law resistance ; conductance Power absorption :

Example 2.1 Determine the current and the power absorbed by the resistor.

Glossary (1) Node A node is simply a point of connection of two or more circuit elements. node Although one node can be spread out with perfect conductors, it is still only one node

(2) loop A loop is simply any closed path through the circuit in which no node is encountered more than once (3) branch  a branch is a single or group of components such as resistors or a source which are connected between two nodes

2. Kirchhoff’s law (1) Kirchhoff ’s current law (KCL) : the algebraic sum of the currents entering(out-going) any node is zero → the sum of incoming currents is equal to the sum of outgoing currents. (2) Kirchhoff’s voltage law (KVL), the algebraic sum of the voltages around any loop is zero

Kirchhoff’s Current law Current definition The direction of a current can be chosen arbitrarily. The value of a current can be obtained from a voltage drop along the direction of current divided by a resistance met. R

Kirchhoff’s Voltage law Sum of voltage drops along a closed loop should be equal to zero! R1 C1 Voltage convention

Example 2.6 Find the unknown currents in the network. Node 1 :

Example E2.6 Find the current ix in the circuits in the figure.

Example E2.8 Find Vad and Veb in the network in the figure.

Example 2.15 Given the following circuit, let us find I, Vbd and the power absorbed by the 30kΩ resistor. Finally, let us use voltage division to find Vbc .

Series resistors equivalent

Parallel resistors equivalent

Example 2.19 Given the circuit, we wish to find the current in the 12-kΩ load resistor. equivalent

Example 2.20 We wish to determine the resistance at terminals A-B in the network in the figure.

Y-Δ transformation Δ Y equivalent

Example 2.26 Given the network in Fig. 2.36a, let us find the source current IS .

2.8 Circuits with dependent sources Example 2.27 Let us determine the voltage Vo in the circuit in the figure.

Example 2.28 Given the circuit in the figure containing a current-controlled current source, let us find the voltage Vo.

Example 2.30 An equivalent circuit for a FET common-source amplifier or BJT common-emitter amplifier can be modeled by the circuit shown in the figure. We wish to determine an expression for the gain of the amplifier, which is the ratio of the output voltage to the input voltage. GND can be arbitrarily set.

Transistor amplifier Transistor

2.10 Application examples Example 2.33 : The Wheatstone bridge circuit.