Lecture Week 4

• Series Circuits

• Parallel Circuits

• Equivalent Circuits

Series Circuit Series Circuits….How do I determine the current through each resistor?

-Current is the same for all resistors

How do I determine the voltage drop through each resistor?

-Voltage is different for all resistors

Series Equivalent Resistance:

𝑹𝒆𝒒 = 𝑹𝟏 + 𝑹𝟐 + 𝑹𝟑 + …𝑹𝒏

Image: Science Buddies Staff, “Squishy Circuits Project 2: Add Even More Lights,” [Online document], 11/21/15, [2/15/16], Available: http://www.sciencebuddies.org/science-fair-projects/project-ideas/Elec_p074/electricity-electronics/squishy-circuits-project-2

V

V

EQUIVALENT

CIRCUIT

VReq

𝐼

Series Circuit - Equivalent Circuit

𝑹𝒆𝒒 = 𝑹𝟏 + 𝑹𝟐 + 𝑹𝟑 + …𝑹𝒏

CURRENT THROUGH ALL RESISTORS IS THE SAME AND

EQUAL TO THE CIRCUIT CURRENT OF THE EQUIVALENT

CIRCUIT

𝑰 =𝑽

𝑹𝒆𝒒

(1) Calculate the Equivalent Resistance (Req).

(2) Use Ohm’s Law to determine the circuit current.

(3) Then use Ohm’s Law to determine the voltage drop across each resistor.

𝑽 = 𝑰𝑹𝟏

Parallel Equivalent Resistance

V

EQUIVALENT

CIRCUIT

𝟏

𝑹𝒆𝒒=

𝟏

𝑹𝟏+

𝟏

𝑹𝟐+

𝟏

𝑹𝒏

𝑰 =𝑽

𝑹𝒆𝒒

(1) Equivalent Resistance (Req)

(2) Current through each Resistor using Ohm’s Law

(3) Voltage drop across each resistor

𝑽 = 𝑽𝟏 = 𝑽𝟐 = 𝑽𝟑

-ALL RESISTORS IN PARALLEL EXPERIENCE THE SAME VOLTAGE DROP

-EQUAL TO THE SUPPLY VOLTAGE OR POWER SUPPLY

-CIRCUIT CURRENT IS SPLIT THROUGH EACH RESISTOR!!!

https://www.youtube.com/watch?v=Oph5JN-ayZ8

𝐼

𝑰 = 𝑰𝟏 + 𝑰𝟐 + 𝑰𝟑

Parallel Resistance: Example

1 K 1 K

I

EE 1305 Name Lab/Team # Date

Calculations:

Problem Statement: Assuming you have two 1 k resistors in parallel, (a) determine the equivalent resistance, (b) the circuit current, (c) the current through each resistor, and (d) add up the currents through each resistor and compare to the circuit current.

Equations/Unit Conversions Figures

1

𝑅𝑒𝑞=

1

𝑅1+

1

𝑅2+

1

𝑅3+ … 𝑉 = 𝐼𝑅

𝑉 = 𝐴

1

𝑅𝑒𝑞=

1

𝑅1+

1

𝑅2

𝑅𝑒𝑞 =𝑅1𝑅2

𝑅1 + 𝑅2

𝑅𝑒𝑞 =1 𝑘 1 𝑘

(1 𝑘+ 1 𝑘)

= 0.5 𝑘

(a)

5VReq = 0.5 k

Parallel Resistance: Example con’t

EE 1305 Name Lab/Team # Date

Calculations 𝑉 = 𝐼𝑅𝑒𝑞

𝐼 =𝑉

𝑅𝑒𝑞=5 𝑉

0.5 𝑘

1 𝑘

103ඍ𝐴

𝑉= 0.01 𝐴

(b)

(c)𝐼 =

𝑉

𝑅1𝑘=5 𝑉

1 𝑘

1 𝑘

103ඍ𝐴

𝑉= 0.005 𝐴

Current through each resistor is 0.005A

(d) 𝐼 = 0.005 𝐴 ∗ 2 = 0.01 𝐴

Adding up the currents gives me the same current as the circuit current.

1 K 1 K

I

5VReq = 0.5 k

I

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

Req = R1 + R2||R3 + R4

R = R2||R3

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||R5Combination of R1 and R2

What’s Next in Week 5?

Will introduce…

LAB• Module 1 – Angle Sensor

LECTURE

• Ohm’s law and its applications: Voltage Divider Method

Please bring laptops to all labs.

P1. 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.

P2 The circuit below includes 3 resistors in parallel, R1 = 1kΩ, R2 = 2 kΩ, and R3 = 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.

P3. (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.

Group Problem:(a) Write the equivalent resistance (Req) using the

shorthand notation for the three resistors. (b) Assume R1 = 1 kΩ, R2

= 1 kΩ, and R3 = 500 Ω, compute the equivalent resistance of the

circuit. (c) Compute the total current I consumed by the circuit (d)

Use Ohm’s law to compute the voltage drop across R3. SHOW ALL

UNITS AND UNIT CONVERSIONS USING THE PROBLEM SOLVING FORMAT

PRACTICED IN CLASS FOR UNIT CONVERSIONS.

What’s Next in Week 5?

Will introduce…

LAB• Module 1 – Angle Sensor

LECTURE

• Ohm’s law and its applications: Voltage Divider Method

Please bring laptops to all labs.

Questions?See you in the next class!