Circuit Elements Voltage and current sources Electrical resistance Kirchhoff’s Laws Resistive Circuits

Voltage and current sources An electrical source is a device that is capable of converting nonelectric energy to electric energy (and vice versa) An ideal voltage source is a circuit element that maintains a prescribed voltage across its terminals regardless of current flowing in these terminals An ideal current source is a circuit element that maintains a prescribed current across its terminals regardless of voltage across the terminals

Ideal voltage source Current-voltage characteristic Circuit symbol

Ideal current source Current-voltage characteristic Circuit symbol

Connections of ideal sources Valid connections

Connections of ideal sources Invalid connections

Connections of ideal sources Valid or invalid?

Electrical resistance Resistance is the capacity of materials to impede the flow of current A resistor is a circuit element that displays this behavior Current-voltage characteristic Circuit symbol

Electrical resistance, cont. Resistor’s obey Ohm’s Law: V = I R The voltage “drop” across a resistor is linearly proportional to the current passing through the resistor

Electrical resistance, cont. Example #1 I = V/R = 5V/1E3W = 5mA

Electrical resistance, cont. Example #2 What is voltage drop across R1 What is voltage polarity?

Kirchhoff’s Laws A node is a point in a circuit where two or more elements meet

Kirchhoff’s current law The algebraic sum of all the currents at any node in a curcuit equals zero I1 + I2 + I3 = 0

Kirchhoff’s voltage law The algebraic sum of all the voltages around any closed path in a circuit equals zero VR3 + VR1 + VR2 + VC0 + VC4 = 0

Resistors in series Using KVL and KCL, we have: -V1 + I*R1 + I*R2 = 0 I*(10 + 20) = 30 ---- I = 30V/30W = 1A

Resistors in series Resistors in series add together This is equivalent to: Rs = R1 + R2 Resistors in series add together

Resistors in parallel Using KVL and KCL, we have: V1 = I1R1 = I2R2 = 10V I1 = 0.100A I2 = 0.033A It = 0.100 + 0.033 = 0.133A

Resistors in parallel Resistors in parallel are This is equivalent to: Resistors in parallel are combined by adding their reciprocals 1/Rp = 1/R1 + 1/R2

Classwork Find (a) the current through R3, (b) the current through R2, and (c) voltage across R1