Lecture Week 5

• Module 1 Follow-up

• Resistive Sensors

• Voltage Divider Method

• The Wheatstone Bridge

• Quiz 2

• Workshop

EE1305/1105 - Weekly Schedule

Next week – Module 2- Strain Gauge (Please bring the print out of the worksheet)

MONDAY TUESDAY WED THURSDAY FRIDAY

7:30 am –10:20 am

LABE301

10:30 am –1:20 pm

LABE301

LABE301

LABE301

3:00 pm –4:20 pm

LectureAnnatoma Arif

BUSN 312

LectureAnnatoma Arif

BUSN 312

Resistive Sensors

• As you have seen in the Angle Sensor lab, there are sensors which measure some real parameter as a change in resistance.

• A thermistor is a resistor, where the value changes with temperature.

• A strain gauge is a resistor, where the value changes with applied strain. You will see the sensor in the next lab.

Voltage Divider Method

The voltage divider is a method/tool that can be used to:

• Design voltage inputs

• Analyze and/or simplify complex circuit

When analyzing a circuit, always determine if the voltage divider method can be used to simplify a circuit!!

Voltage Divider MethodThe voltage divider relates the total voltage to the potential drop across one of the resistors.

𝒗𝒊 = 𝒗𝒔𝑹𝒊

𝑹𝒆𝒒

𝑉1 = 𝐼 𝑅1 =𝑉𝑠

𝑅1 + 𝑅2

𝑅1= 𝑉𝑠

𝑅1𝑅1 + 𝑅2

𝑅𝑒𝑞 = 𝑅1 + 𝑅2

𝐼 =𝑉𝑠

𝑅𝑒𝑞=

𝑉𝑠

𝑅1+𝑅2

𝑉2 = 𝐼 𝑅2 =𝑉𝑠

𝑅1 + 𝑅2

𝑅2= 𝑉𝑠

𝑅2𝑅1 + 𝑅2

VOLTAGE DIVIDER METHOD CAN SAVE A TIME WHEN DESIGNING CIRCUITS

Voltage Divider Method: Exercise 1Determine the voltage drop across BOTH R1 and R2, based on the following component values:

Vs = 5 V, R1 = 1 M, and R2 = 725 k

𝒗𝒊 = 𝒗𝒔𝑹𝒊

𝑹𝒆𝒒

TIP: IN THIS CASE, IT HELPS TO CONVERT YOUR UNITS TO OHMS () BEFORE PLUGGING IN VALUES INTO EQUATION.

Voltage Divider Method: Exercise 2Assume R1, R2, R3 and R4 are all equal to 121 .

(a) Determine the equivalent resistance for R3||R5 based on the 3 values for R5 listed in the table below.

(b) Use the Voltage Divider method to determine the voltage

drop across R4 based on R3||R5 equivalent value.

R5, R3||R5, Voltage Drop Across R4, V

100,000

499,000

1,000,000

Voltage Divider Method: Analyzing Exercise 2• What happens to the value of R3||R5 as R5 is increased? Complete

this statement:

“When there are two resistors in parallel, and on

of those resistors increased, the equivalent

resistance ______________.

R5, R3||R5,

100,000

499,000

1,000,000

[INCREASES/DECREASES]

Voltage Divider Method: Analyzing Exercise 2• What happens to the value of R4 as R5 is increased? Complete this

statement:

“When R5 is increased, the equivalent resistance of

R3||R5 ______________, and the voltage drop across

R4 _____________.

R5, R3||R5,

100,000 120.8538

499,000 120.9707

1,000,000 120.9854

[INCREASES/DECREASES]

[INCREASES/DECREASES]

𝒗𝒊 = 𝒗𝒔𝑹𝒊

𝑹𝒆𝒒

Voltage Divider and Shorthand Notation: Exercise 3(a) Simplify the circuit below using equivalent parallel/series resistance and voltage

divider to determine VA. As you simplify the circuit, RE-SKETCH the equivalent circuit and label the equivalent resistor values using SHORTHAND NOTATION.

(b) Determine the current through R3 ( I3)

Vin = 5 VR1 = 125 ΩR2 = 220 ΩR3 = 500 Ω

• Please clear desks and turn off phones and put them in backpacks.

• You need pen/pencil, straight edge and calculator.

• 15 minutes

• Keep eyes on your own paper.

• Follow same format as for homework.

• Turn in your completed quiz at the front of the room.

• When you finish, please sit quietly until everyone is finished.

Quiz 2

Questions?See you in the next class!

HWP1. Using Ohm’s Law, [a] calculate the equivalent resistance Req [b] find the total current (I) and [c]the voltage drops for R2 for the circuit below. [d] Calculate the power absorbed by for R1. SHOW ALL UNITS AND UNIT CONVERSIONS USING THE FORMAT TAUGHT IN THE CLASS.

HWP2 – You step out of the room and your lab mate changes the resistors on your circuit.

Since the three resistors are in series, the current flowing through each resistor is the same.

(a) Compute the equivalent resistance Req of the circuit (redraw it).

(b) Use Ohm’s Law to compute the new current value.

(b) Determine the new voltage drop across each resistor.

(b) Find the power consumed by each resistor (R1, R2 and R3).

HWP3 (a) Simplify the circuit and determine the equivalent resistance. (b) Determine the circuit current, and(c) Determine the power consumed by the equivalent resistance and the power supplied by the 12 V source. (d) Does conservation of power exist in the circuit? Label each step and include units and unit conversions for full credit.

P1(a) Simplify the circuit below using equivalent parallel/series resistance and

voltage divider to determine VA and VB. As you simplify the circuit, RE-SKETCH the equivalent circuit and label the equivalent resistor values using SHORTHAND NOTATION.

(b) Determine the current through R2 ( I2)

Vin = 10 VR1 = 125 ΩR2 = 220 ΩR3 = 500 ΩR4 = 100Ω

P2(a) Use the shorthand notation/equivalent circuit method to reduce the circuit until

there are only 2 resistors left. For each step, show the equivalent circuit, and write the shorthand notation expression.

(b) (b) When there are only 2 resistors left, determine the expression for the voltage drop at VA using the voltage divider method. Make sure to include the equation for voltage divider at the beginning of this step.

Group Problem(a) Determine the circuit total current (IT) for the simplified circuit in P2 if R1–R4 are equal to 100Ω and Vin is equal to 9 V.

(b) Use Ohm’s Law to confirm the voltage drop at VA.

(c) Use the expression for P2 part (b) to determine VA using the voltage divider method. Show every step, units, and unit conversions for full credit.

What’s Next in Week 6?

Will introduce…

LAB

• Module 2 – Strain Gauge

LECTURE

• Quiz 3 - Kirchhoff's Laws

Please bring laptops to all labs.

Voltage Divider and Shorthand Notation - Solutions

Questions?See you in the next class!