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ENGR 111 Lecture 4 Reading: Chapters 19, Class notes

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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)

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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

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Some basic laws (Kirchoff) Kirchoff’s Current Law (KCL): Current flowing into and out of a node should be equal Conservation principle

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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 Start End V1 V2 V3 V4 V5 V1 + V2 + V3 +V4 + V5 = 0

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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 Ohm’s Law

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Resistors Connected in series I I R1 R2 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

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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 = ?

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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. R1 R2 I I1 I2 I

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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

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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)

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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) I I1 I2 R1 R2

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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?

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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?

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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

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Example 1: KVL & Ohm’s Law

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Example 2: Resistors

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Example 3: Resistors

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Example 4: Voltage Divider

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Example 5: Current Divider

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