Lecture Week 4 Homework Voltage Divider Equivalent Circuit Observation Exercise
Homework: P6 Prove that the equation relating change in potential energy to voltage is dimensionally consistent, using the unit conversions provided below.
Homework: P8 Calculate the equivalent resistance for the resistors in series. Use the equivalent resistance to determine the current flowing through each resistor. Make sure to show the unit conversion V = AΩ when setting up your current (I) calculation. Show all units and unit conversions for each calculation.
Homework: P9 The circuit below includes 3 resistors in parallel, R 1 = 1kΩ, R 2 = 2 kω, and R 3 = 4 kω. (a) Determine the equivalent resistance (Req), (b) use Ohm s Law to determine the circuit current, (c) use Ohm s Law to determine the current through each resistor.
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 Method The voltage divider relates the total voltage to the potential drop across one of the resistors. R eq = R 1 + R 2 I = V s R eq = V s R 1 +R 2 V 1 = I R 1 = V s R 1 + R 2 R 1 = Vs R 1 R 1 + R 2 v i = v s R i R eq V 2 = I R 2 = V s R 1 + R 2 R 2 = Vs R 2 R 1 + R 2 VOLTAGE DIVIDER METHOD VERY POWERFUL TOOL USED TO ANALYZE CIRCUITS!!!
Voltage Divider Method: Exercise 1 Determine the voltage drop across BOTH R 1 and R 2, based on the following component values: Vs = 5 V, R 1 = 1 M, and R 2 = 725 k v i = v s R i R eq TIP: IN THIS CASE, IT HELPS TO CONVERT YOUR UNITS TO OHMS ( ) BEFORE PLUGGING IN VALUES INTO EQUATION.
Voltage Divider Method: Exercise 2 Assume 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. [INCREASES/DECREASES] R5, R3 R5, 100,000 499,000 1,000,000
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 [INCREASES/DECREASES] R3 R5, and the voltage drop across R4. [INCREASES/DECREASES] R5, R3 R5, 100,000 120.8538 499,000 120.9707 1,000,000 120.9854 v i = v s R i R eq
Shorthand Notation/Equivalent Circuits: Series Resistors Req = R1 + R2 + R3
Shorthand Notation/Equivalent Circuits: Parallel Resistors Req = R1 R2 R3
Shorthand Notation/Equivalent Circuits: Combination Resistors R = R2 R3 Req = R1 + R2 R3 + R4
Shorthand Notation/Equivalent Circuits: Example Simplify each side of the circuit.
Shorthand Notation/Equivalent Circuits: Example Combination of R3 and R5 Combination of R4 and R3 R5 Combination of R1 and R2
Voltage Divider and Shorthand Notation: Exercise 3 (a) Simplify the circuit below using equivalent parallel/series resistance and voltage divider to determine V A (b) Determine the current through R 3 ( I 3 ) (c) As you simplify the circuit, RE-SKETCH the equivalent circuit and label the equivalent resistor values using SHORTHAND NOTATION. V in = 5 V R 1 = 125 Ω R 2 = 220 Ω R 3 = 500 Ω
Voltage Divider and Shorthand Notation: Exercise 4 (a) Simplify the circuit below using equivalent parallel/series resistance and voltage divider to determine V A and V B (b) Determine the current through R 2 ( I 2 ) (c) As you simplify the circuit, RE-SKETCH the equivalent circuit and label the equivalent resistor values using SHORTHAND NOTATION. V in = 10 V R 1 = 125 Ω R 2 = 220 Ω R 3 = 500 Ω R 4 = 100Ω
Voltage Divider and Shorthand Notation - Solutions
Homework- Due 9/25 (Najera), due 9/28 (Martinez- Acosta) P10, P11 and P12
Observation Exercise The method relates the potential drop across one of the resistors to the total voltage. The equivalent circuit introduced in Exercise 2 can include voltage dividers calculations.
What s Next in Week 5? Will introduce LAB Handling Op-Amps Building Op-Amps Observation Exercise LECTURE Quiz 2 Ohm s Law Ideal Op-amp theory Observation Exercise Please bring laptops to all lectures and labs.
Questions?