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Exploring Electric Circuits: Resistors, EMF, and Current Analysis

Learn about resistors in series and parallel, EMF, Kirchhoff’s rules, and instrument use in electric circuits. Understand how current, voltage, and resistance interact in circuits. Enhance your knowledge of RC circuits and internal resistance effects.

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Exploring Electric Circuits: Resistors, EMF, and Current Analysis

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  1. Electric Current & Circuits PHY2054: Chapter 21 (OpenStax)

  2. Chapter 21: Electric Circuits, Instruments • Resistors in series and parallel • EMF and terminal voltage • Kirchhoff’s rulesand multi-loop circuits • Ammeters and voltmeters • Null measurements • RC circuits (resistors and capacitors in the same circuit) PHY2054: Chapter 21 (OpenStax)

  3. Reading Quiz for Chapter 21 • When resistors are connected in series • (1) the current in each resistor is different • (2) the current in each resistor is the same • (3) the voltage in each resistor is the same PHY2054: Chapter 21 (OpenStax)

  4. Reading Quiz for Chapter 21 • When resistors are connected in series • (1) the current in each resistor is different • (2) the current in each resistor is the same • (3) the voltage in each resistor is the same PHY2054: Chapter 21 (OpenStax)

  5. Reading Quiz for Chapter 21 • Which of the following is not related to Kirchhoff’s Rules? • (1) conservation of charge • (2) conservation of energy • (3) conservation of momentum PHY2054: Chapter 21 (OpenStax)

  6. Reading Quiz for Chapter 21 • Which of the following is not related to Kirchhoff’s Rules? • (1) conservation of charge • (2) conservation of energy • (3) conservation of momentum PHY2054: Chapter 21 (OpenStax)

  7. Series Circuit • Simple series situation • 1 battery and two resistors R1 and R2 • Common current I • Total voltage E = V1 + V2 • E = IR1 + IR2≡IRs • Rs = R1 + R2 • So equivalent resistance is the sum • Works for any number of resistors • Rs = R1 + R2 + R3 + R4 + … E PHY2054: Chapter 21 (OpenStax)

  8. Resistors in series • Battery EMF = 12 V, 3 identical resistors.What is the potential difference across each resistor? • 12 V • 0 V • 3 V • 4 V R R R PHY2054: Chapter 21 (OpenStax)

  9. Resistors in series Current is the same, so voltage across each is the same R R R • Battery EMF = 12 V, 3 identical resistors.What is the potential difference across each resistor? • 12 V • 0 V • 3 V • 4 V PHY2054: Chapter 21 (OpenStax)

  10. A B Resistors in Series • If the light bulbs are all the same in each of these two circuits, which circuit has the higher current? • (1) circuit A • (2) circuit B • (3) both the same PHY2054: Chapter 21 (OpenStax)

  11. A B Resistors in Series • If the light bulbs are all the same in each of these two circuits, which circuit has the higher current? • (1) circuit A • (2) circuit B • (3) both the same A has twice the current as B PHY2054: Chapter 21 (OpenStax)

  12. Real EMF Sources: Internal Resistance • Real batteries have small internal resistance • Lowers effective potential delivered to circuit E This is the voltage measured across the terminals! PHY2054: Chapter 21 (OpenStax)

  13. Internal Resistance Example • Loss of voltage is highly dependent on load • E = 12V, r = 0.1Ω, R = 100Ω • Loss of 0.01V • E = 12V, r = 0.1Ω, R = 10Ω • Loss of 0.1V • E = 12V, r = 0.1Ω, R = 1Ω • Loss of 1.1V • E = 12V, r = 0.1Ω, R = 0.5Ω • Loss of 2.0V PHY2054: Chapter 21 (OpenStax)

  14. Resistors in Parallel I • Current splits into several branches. Total current is conserved • I = I1 + I2 • Potential difference is same across each resistor • V = V1 = V2 a I1 I2 V R1 R2 I d I a I V Rp I d Rp = equivalent resistance. Works for any number of resistors PHY2054: Chapter 21 (OpenStax)

  15. Resistors in Parallel • As more resistors R are added in parallel to the circuit, how does total resistance between points P and Q change? • (a) increases • (b) remains the same • (c) decreases PHY2054: Chapter 21 (OpenStax)

  16. Resistors in Parallel • As more resistors R are added in parallel to the circuit, how does total resistance between points P and Q change? • (a) increases • (b) remains the same • (c) decreases PHY2054: Chapter 21 (OpenStax)

  17. Resistors in Parallel • If the voltage between P & Q isheld constant, and more resistorsare added, what happens tothe current through each resistor? • (a) increases • (b) remains the same • (c) decreases PHY2054: Chapter 21 (OpenStax)

  18. Resistors in Parallel • If the voltage between P & Q isheld constant, and more resistorsare added, what happens tothe current through each resistor? • (a) increases • (b) remains the same • (c) decreases For each branch PHY2054: Chapter 21 (OpenStax)

  19. Resistance Example • Find net resistance of the circuit connected to the battery. Each resistance has R = 3 kΩ Note that in the followingfigures that kΩ displays as kW for some reason. PHY2054: Chapter 21 (OpenStax)

  20. Resistance Example (1+2) • Combine #1 & #2 in series • R12 = 3 + 3 = 6 kΩ Note that kΩ displays as kW. PHY2054: Chapter 21 (OpenStax)

  21. Resistance Example (1+2+3) • Combine 6kΩ & #3 in parallel • R123 = 6 || 3 = 2 kΩ PHY2054: Chapter 21 (OpenStax)

  22. Resistance Example (1+2+3+4) • Combine 2kΩ & #4 in series • R1234 = 2 + 3 = 5 kΩ PHY2054: Chapter 21 (OpenStax)

  23. Resistance Example (1+2+3+4+5) • Combine 5kΩ & #5 in parallel • R12345 = 5 || 3 = 1.875 kΩ PHY2054: Chapter 21 (OpenStax)

  24. Resistance Example (1+2+3+4+5+6) • Combine 1.875kΩ & #6 in series • R123456 = 1.875 + 3 = 4.875 kΩ PHY2054: Chapter 21 (OpenStax)

  25. A B Circuits • If the light bulbs are all the same in each of these two circuits, which circuit has the higher current through the battery? • (a) circuit A • (b) circuit B • (c) both the same PHY2054: Chapter 21 (OpenStax)

  26. A B Circuits • If the light bulbs are all the same in each of these two circuits, which circuit has the higher current through the battery? • (a) circuit A • (b) circuit B • (c) both the same B draws twice the current as A PHY2054: Chapter 21 (OpenStax)

  27. A B Circuits • In which circuit is each light bulb brighter? • (a) circuit A • (b) circuit B • (c) both the same PHY2054: Chapter 21 (OpenStax)

  28. A B Circuits • In which circuit is each light bulb brighter? • (a) circuit A • (b) circuit B • (c) both the same Current through each branch is unchanged (V / R) PHY2054: Chapter 21 (OpenStax)

  29. Household Circuits: Parallel Paths! • All devices are added in parallel • Each power outlet is 115 V, independently of others • Enough power must be supplied from connection to power company • Overload: too many devices that require a lot of current can draw more current than wires can handle. • Overheating of wires • Fire hazard! PHY2054: Chapter 21 (OpenStax)

  30. Circuit Problem (1) • The light bulbs in the circuit are identical. What happens when the switch is closed? • a) both bulbs go out • b) the intensity of both bulbs increases • c) the intensity of both bulbs decreases • d) nothing changes 12V (b) (a) 12V PHY2054: Chapter 21 (OpenStax)

  31. Circuit Problem (1) • The light bulbs in the circuit are identical. What happens when the switch is closed? • a) both bulbs go out • b) the intensity of both bulbs increases • c) the intensity of both bulbs decreases • d) nothing changes 12V (b) (a) Before switch closed: Va = 12V because of battery. Vb =12 because equal resistance divides 24V in half. After switch closed: Nothing changessince (a) and (b) are still at same potential. 12V PHY2054: Chapter 21 (OpenStax)

  32. Circuit Problem (2) • The light bulbs in the circuit shown below are identical. When the switch is closed, what happens to the intensity of the light bulbs? • a) bulb A increases • b) bulb A decreases • c) bulb B increases • d) bulb B decreases • e) nothing changes 12V (b) (a) 12V 12V PHY2054: Chapter 21 (OpenStax)

  33. Circuit Problem (2) • The light bulbs in the circuit shown below are identical. When the switch is closed, what happens to the intensity of the light bulbs? • a) bulb A increases • b) bulb A decreases • c) bulb B increases • d) bulb B decreases • e) nothing changes 12V (b) (a) 12V 12V Before switch closed: Va = 12V because of battery. Vb =12 because equal resistance divides 24V in half. After switch closed: Nothing changessince (a) and (b) are still at same potential. PHY2054: Chapter 21 (OpenStax)

  34. Circuit Problem (3) • The bulbs A and B are identical. What happens when the switch is closed? • a) nothing happens • b) A gets brighter, B dimmer • c) B gets brighter, A dimmer • d) both go out 12V (a) (b) 24V PHY2054: Chapter 21 (OpenStax)

  35. Circuit Problem (3) • The bulbs A and B are identical. What happens when the switch is closed? • a) nothing happens • b) A gets brighter, B dimmer • c) B gets brighter, A dimmer • d) both go out 12V (a) (b) Before: Va = 24, Vb = 18. Bulb A and bulb B both have 18V across them. After: Va = 24, Vb = 24 (forced by the batteries).Bulb A has 12V across it and bulb B has 24V across it. 24V PHY2054: Chapter 21 (OpenStax)

  36. Using Kirchhoff’s Rules (1) • Junction rule (conservation of current/charge) • Current into junction = sum of currents out of it I1 I I2 I3 PHY2054: Chapter 21 (OpenStax)

  37. Using Kirchhoff’s Rules (2) • Loop rule (conservation of energy) • Algebraic sum of voltages around a closed loop is 0 1 2 1 2 PHY2054: Chapter 21 (OpenStax)

  38. Problem Solving Using Kirchhoff’s Rules • Label the current in each branch of the circuit • Choice of direction is arbitrary • Signs will work out in the end (if you are careful!!) • Apply the junction rule at each junction • Keep track of sign of currents entering and leaving • Apply loop rule to each loop (follow in one direction only) • Resistor: loop direction same as current direction: ⇒ –iR • Resistor: loop direction opposite current direction: ⇒ +iR • Battery: loop direction in “normal” direction: ⇒ +V • Battery: loop direction in “opposite”direction: ⇒ –V • Solve equations simultaneously • You need as many equations as you have unknowns PHY2054: Chapter 21 (OpenStax)

  39. Kirchhoff’s Rules: Example • Determine the magnitudes and directions of the currents through the two resistors in the figure below. • Take two loops, 1 and 2, as shown on next slide 2 1 PHY2054: Chapter 21 (OpenStax)

  40. Kirchhoff’s Rules: Example • Determine the magnitudes and directions of the currents through the two resistors in the figure below. • Take two loops, 1 and 2, as shown 1 2 2 1 Currents are all +, so are in directions shown PHY2054: Chapter 21 (OpenStax)

  41. Circuit Quiz • Which of the equations is valid for the circuit shown below? • a) 2 − I1− 2I2 = 0 • b) 2 − 2I1− 2I2− 4I3 = 0 • c) −2 − I1− 4 − 2I2 = 0 • d) I3− 2I2− 4I3 = 0 • e) 2 − 2I1− 2I2− 4I3 = 0 PHY2054: Chapter 21 (OpenStax)

  42. Circuit Quiz • Which of the equations is valid for the circuit shown below? • a) 2 − I1− 2I2 = 0 • b) 2 − 2I1− 2I2− 4I3 = 0 • c) −2 − I1− 4 − 2I2 = 0 • d) I3− 2I2− 4I3 = 0 • e) 2 − 2I1− 2I2− 4I3 = 0 PHY2054: Chapter 21 (OpenStax)

  43. Resistors • Current flows through a light bulb. If a wire is now connected across the bulb as shown, what happens? • (a) All the current continues to flow through the bulb • (b) Current splits 50-50 into wire and bulb • (c) Almost all the current flows through the wire • (d) None of the above PHY2054: Chapter 21 (OpenStax)

  44. Resistors • Current flows through a light bulb. If a wire is now connected across the bulb as shown, what happens? • (a) All the current continues to flow through the bulb • (b) Current splits 50-50 into wire and bulb • (c) Almost all the current flows through the wire • (d) None of the above Current is maintained by external voltage source. The wire “shunt” has almost no resistance andit is in parallel with a bulb having resistance.Therefore all the current follows the zero (orextremely low) resistance path. PHY2054: Chapter 21 (OpenStax)

  45. Circuit Example (1) • Consider the network of resistors shown below. The switch is initially open, then closed. • What happens to the currentwithin and voltage across R1? • What happens to the current within and voltage across R2, R3, R4? • What happens to the total power output of the battery? PHY2054: Chapter 21 (OpenStax)

  46. Circuit Example (2) • Consider the network of resistors shown below. The switch is initially open, then closed. • What happens to the currentand voltage through R1? • After switch closes: • More resistors in parallel • Parallel resistance decreases • Current through R1 increases • Voltage across R1 increases PHY2054: Chapter 21 (OpenStax)

  47. Circuit Example (3) • Consider the network of resistors shown below. The switch is initially open, then closed. • What happens to the current and voltagein R2, R3, R4? • Voltage across R1 increases • Voltages across R2, R3, R4 thus decrease • Current in R2 increases (from 0) • Currents in R3 & R4 decrease PHY2054: Chapter 21 (OpenStax)

  48. Circuit Example (4) • Consider the network of resistors shown below. The switch is initially open, then closed. • What happens to the total power output of battery? • After switch closes: • Same emf, more current • Power = Emf * i increases PHY2054: Chapter 21 (OpenStax)

  49. Circuit Example (5) • Consider the network of resistors shown below. The switch is initially open, then closed. • Let R1 = R2 = R3 = R4 = 90Ω and V = 45 V. • Initial total resistance is 90Ω + 45Ω = 135Ω, final is 90Ω + 30Ω = 120Ω • Find current through each resistor before and after closing the switch. • Before • I1 = 45/135 = 1/3 • I2 = 0 • ΔV1 = I1*R1= 30, ΔV2 = 0 • ΔV3 = ΔV4 = 45 – 30 = 15 • I3= I4 = 15/90=1/6 • After • I1 = 45/120 = 3/8 • ΔV1 = I1*R1 = 33.75 • ΔV2 = ΔV3 = ΔV4 = 11.25 • I2= I3 = I4 = 1/8 PHY2054: Chapter 21 (OpenStax)

  50. Wheatstone Bridge • An ammeter A is connected between points a and b in the circuit below. What is the current through the ammeter? • a) I / 2 • b) I / 4 • c) zero • d) need more information a R R R R I b V PHY2054: Chapter 21 (OpenStax)

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