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ENGR 111 Lecture 4. Reading: Chapters 19, Class notes. Lecture 4: DC Fundamentals . Review of Last Class: More/less electrons => Charge Potential charge difference results in charge flow or current Potential charge difference = voltage
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ENGR 111 Lecture 4 Reading: Chapters 19, Class notes
Lecture 4: DC Fundamentals • Review of Last Class: • More/less electrons => Charge • Potential charge difference results in charge flow or current • Potential charge difference = voltage • Different materials offer different resistance to current • Voltage V(volts), Current I (Amperes), Resistance R (ohms)
Water Analogy • Charge flow through a wire similar to water flow in a pipe • Harder to push water through a thinner pipe (smaller current, higher resistance) • For water to flow, there has to be pressure difference at ends of pipe • Voltage has to exist across a wire for current
Some basic laws (Kirchoff) • Kirchoff’s Current Law (KCL): • Current flowing into and out of a node should be equal • Conservation principle
Kirchoff’s voltage Law • Voltages around a closed circuit should sum to zero • When you come to the same point, voltage difference should be zero V2 V1 V3 Start End V5 V4 V1 + V2 + V3 +V4 + V5 = 0
Ohm’s Law • Ohm’s law relates resistance, voltage and current V = I * R • Higher resistance, need higher voltage for the same amount of current to flow • Water Analogy, higher pressure at ends of pipe, higher flow of water
I I R2 R1 Ohm’s Law • Resistors Connected in series • KCL => current entering R1 must leave R1 • Current entering R2 = current leaving R1 • V1 = I * R1, V2 = I *R2 • V = V1 + V2 = I * R1 + I * R2 = I (R1+R2) = IR • Resistors in series R = R1 + R2
Resistors in Series • 100 ohms in series with 100 ohms = 200 ohms equivalent resistance • 100 ohms in series with 1 ohm = ? • 101 ohms from the calculator • 100 ohms taking significant digits into account • Resistors are calibrated to 5 or 10% accuracy • 100 ohms in series with 100 ohms = ? • 100 ohms in series with 1M ohms = ?
I1 R1 I I I2 R2 Resistors in Parallel • The current gets divided among the two paths. • KVL tells us V = I1 * R1 = I2 * R2 • KCL => I = I1 + I2 = V/R1 + V/R2 = V (1/R1 + 1/R2) • I = V (R2 + R1)/R1R2 • V = I (R1 * R2)/(R1 + R2) • Equivalent Resistance R = R1 * R2/(R1 + R2) • Easier to Remember 1/R = 1/R1 + 1/R2 • Voltage across the two resistors must be equal.
Resistors in Parallel • 100 ohms in parallel with 100 ohms • 1/R = 1/100 + 1/100 = 2/100 = 1/50 • R = 50 ohms, Resistance is smaller!! • Water Analogy, two pipes in parallel, more opportunity for water to flow, less resistance • 100 ohms in parallel with 1000 ohms • 1/R = 1/100 + 1/1000, R = 90.90 = 91Ω
Voltage Dividers • Resistors in series provide a mechanism • The resistors determine the output Voltage • KCL says same current in R1 and R2 • Vout = V1 * R2/(R1+R2)
Current Dividers • Resistors in parallel provide a mechanism • The resistors determine the current in each path • I1 * R1 = I2 * R2, I2 = I1 * R1/R2 • I = I1 + I2 => I1 = I * R2/(R1+R2) I1 R1 I I2 R2
Example Dividers • Given 10V, Need to provide 3V, how? • Resistors in Series • R2/(R1+R2) = 3/10, choose R2 = 300 KΩ • R1 = 700 KΩ • Why should R1, R2 be high? • What happens when we connect a resistor R3 across R2?
Example Dividers • Want to divide current into two paths, one with 30% --how? • Resistors in parallel • R2/(R1+R2) = 0.3, Choose R2 = 300 KΩ • R1 = 700 KΩ • Why should R1, R2 be high? • What happens when we connect a resistor R3 in series with R2?
Summary • Ohm’s Law V = I * R • KCL/KVL and Ohm’s law allow us to compute equivalent resistances • Resistances in series R = R1 + R2 • Resistances in parallel 1/R = 1/R1 + 1/R2 • Resistances in series => Voltage Dividers • Resistances in parallel => Current dividers
