E E 1205 Circuit Analysis Lecture 03 - Simple Resistive Circuits and Applications

Calculating Resistance When conductor has uniform cross-section

Temperature Coefficient of Resistance Metallic conductors have a linear increase of resistance with increased temperature. T o is the reference temperature (usually 20 o C) and R o is the resistance at the reference temperature.  is the temperature coefficient of resistance for the material. At 20 o C, some values for  are: 20 o C Aluminum Copper

Resistors in Series By KCL: I s = I 1 = I 2 By Ohm’s Law: V 1 = R 1 ·I 1 and V 2 = R 2 ·I 2 Combine: V s = R 1 I 1 + R 2 I 2 = (R 1 + R 2 ) I s = R eq I s In General: R eq = R 1 + R 2 +···+ R n

Resistors in Parallel (1/2) By KVL: V s = V 1 = V 2 By KCL: I s = I 1 + I 2 By Ohm’s Law: and Combine:

Resistors in Parallel (2/2) For two resistors: For many resistors: In terms of conductance:

Voltage Divider Circuit

Loaded Voltage Divider

Voltage Divider Equations Unloaded: Loaded: If R L >> R 2 :