ENGR 111 Lecture 4

Reading: Chapters 19, Class notes

Lecture 4: DC Fundamentals

Review of Last Class:More/less electrons => ChargePotential charge difference results in

charge flow or currentPotential charge difference = voltageDifferent materials offer different

resistance to currentVoltage 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

Start

End

V1V2

V3

V4

V5

V1 + V2 + V3 +V4 + V5 = 0

Ohm’s law relates resistance, voltage and current

V = I * RHigher resistance, need higher voltage for

the same amount of current to flowWater Analogy, higher pressure at ends of

pipe, higher flow of water

Ohm’s Law

Ohm’s Law

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

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 = ?

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

II1

I2

I

Resistors in Parallel

100 ohms in parallel with 100 ohms1/R = 1/100 + 1/100 = 2/100 = 1/50R = 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 ohms1/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 mechanismThe resistors determine the current in

each pathI1 * R1 = I2 * R2, I2 = I1 * R1/R2I = I1 + I2 => I1 = I * R2/(R1+R2)

I

I1

I2

R1

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 parallelR2/(R1+R2) = 0.3, Choose R2 = 300 KΩR1 = 700 KΩWhy should R1, R2 be high?What happens when we connect a resistor

R3 in series with R2?

Summary

Ohm’s Law V = I * RKCL/KVL and Ohm’s law allow us to

compute equivalent resistancesResistances in series R = R1 + R2Resistances in parallel 1/R = 1/R1 + 1/R2Resistances in series => Voltage DividersResistances in parallel => Current dividers

Example 1: KVL & Ohm’s Law

1 2 0 V IR IR

Example 2: Resistors

2

2 3 V V V R

IR R I

Example 3: Resistors

1

31 2

1 23

1 2

1 1

ABR RR R

R RR

R R

Example 4: Voltage Divider

2 1

1 2 1 2

, BC AB

R RV V V V

R R R R

Example 5: Current Divider

2 2I

I