1 / 19

Electrical Circuits and Current Analysis

Learn about electric currents, EMF devices, Kirchhoff's rules, and how to analyze circuits. Understand the role of ammeters and voltmeters in measuring currents and potential differences.

nhorn
Download Presentation

Electrical Circuits and Current Analysis

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Magnitude rate at which net positive charges move across a cross sectional surface Units:[I] = C/s = A (ampere) Current is ascalar, signed quantity, whose sign corresponds to the direction ofmotion of netpositive charges by convention Electric Current Current = charges in motion J = current density (vector) in A/m²

  2. R I V constant ROhm’s Law Power dissipation : Ohm’s Law Resistance (definition)

  3. EMF – Electromotive Force • An EMF device is a charge pump that can maintain a potential difference across two terminals by doing work on the charges when necessary. Examples:battery, fuel cell, electric generator, solar cell, fuel cell, thermopile, … • Converts energy (chemical, mechanical, solar, thermal, …) into electrical energy. • Within the EMF device, positive charges are lifted from lower to higher potential. • If work dW is required to lift charge dq, EMF

  4. i Req i R1 R2 i ε ε For multiple resistors in series: Resistors in Series • The current through devices in series is always the same. Same equation for parallel connected capacitors

  5. i Req ε terminal voltage internal resistance Real Battery = Resistors in Series • The current through devices in series is always the same.

  6. Devices in parallel has the same potential drop Generally, Resistors in Parallel Same equation for capacitors connected in serial

  7. Kirchhoff’s Rule 1: Loop Rule • When any closed loop is traversed completely in a circuit, the algebraic sum of the changes in potential is equal to zero. Kirchhoff’s Rule 2: Junction Rule • The sum of currents entering any junction in a circuit is equal to the sum of currents leaving that junction. Kirchhoff’s Rules • Coulomb force is conservative • Conservation of charge • In and Out branches • Assign Ii to each branch

  8. Circuit Analysis Tips • Simplify using equivalent resistors • Label currents with arbitary directions • If the calculated current is negative, the real direction is opposite to the one defined by you. • Apply Junction Rule to all the labeled currents. • Useful when having multiple loops in a circuit. • Choose independent loops and define loop direction • Imagine your following the loop and it’s direction to walk around the circuit. • Use Loop Rule for each single loop • If current I direction across a resistor R is the same as the loop direction, potential drop across R is ∆V = −I×R, otherwise, ∆V = I×R • For a device, e.g. battery or capacitor, rely on the direction of the electric field in the device and the loop direction to determine the Potential drop across the device • Solve simultaneous linear equations

  9. Þ Loop Example with Two EMF Devices If 1 <2, we have I<0 !? This just means the actual current flows reverse to the assumed direction. No problem!

  10. Just means 0 V here Finding Potential and Power in a Circuit But what is I? Must solve for I first! supplied by 12V battery dissipated by resistors The rest? into 4V battery (charging)

  11. good battery (12V) battery being charged (11V) power into battery 2 Charging a Battery • Positive terminal to positive terminal • Charging EMF > EMF of charged device Say, R+r1+r2=0.05 (R is for jumper cables). Then, • If connected backward, • Large amount of gas produced • Huge power dissipation in wires

  12. Identify nodes and use Junction Rule: Only two are independent. Using Kirchhoff’s Laws in Multiple Loop Circuits • Identify independent loops and use Loop Rule:

  13. I1+I2 I2 I1 Warm-up quiz • What’s the current I1 ? (a). 2.0A (b). 1.0A (c). -2.0A (d). -1.0A (e). Need more information to calculate the value.

  14. I1+I2 I2 I1 Replace by equivalent R=2 first. Answer for the Warm-up quiz • Sketch the diagram • Simplify using equivalent resistors • Label currents with directions • Use Junction Rule in labeling • Choose independent loops • Use Loop Rule • Solve simultaneous linear equations

  15. Ammeter and Voltmeter • Ammeter: an instrument used to measure currents • It must be connected in series. • The internal resistance of an ammeter must be kept as small as possible. • Voltmeter: an instrument used to measure potential differences • It must be connected in parallel. • The internal resistance of a voltmeter must be made as large as possible.

  16. galvanometer shunt resistor Galvanometer Inside Ammeter and Voltmeter Galvanometer: a device that detects small currents and indicates its magnitude. Its own resistance Rgis small for not disturbing what is being measured. Ammeter: an instrument used to measure currents Voltmeter: an instrument used to measure potential differences galvanometer

  17. PHYS241 – Quiz 11A What is the current through R1 ? 30 30 • 0.575A • 0.5A • 0.75A • 0.33A • 1.5A R1 R2 45V 45V R3 30

  18. PHYS241 – Quiz11B What is the current through R2 ? 10 10 • 0.33A • 2.5A • 0.75A • 1.5A • 0.5A R1 R2 15V 15V R3 10

  19. PHYS241 – Quiz 11C What is the current through R3 ? 20 20 • 0.375A • 0.5A • 0.75A • 1A • 1.5A R1 R2 30V 30V R3 20

More Related