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Ohm’s Law

Ohm’s Law. Objective: TSW understand the concepts of Voltage, Current, and Resistance by developing and applying Ohm’s Law. Circuit simulation. I. I. I. R. I. I. I. I. V. V = Voltage = A potential difference that motivates charge to flow. The pump. (units: V = J/C).

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Ohm’s Law

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  1. Ohm’s Law Objective: TSW understand the concepts of Voltage, Current, and Resistance by developing and applying Ohm’s Law.

  2. Circuit simulation

  3. I I I R I I I I V V = Voltage = A potential difference that motivates charge to flow. The pump. (units: V = J/C) I = current = The amount of charge that flows per unit time. (units: C/s = Amps A) R = Resistance = A property of the material that resists the flow of current. (units: Ohms Ω = V/A)

  4. V and R R V and Let’s learn how these three quantities are related by imaging different Voltages with a constant Resistance. Predict the current with a large voltage and a small resistance: I Predict the current with a small voltage and a large resistance: I

  5. V =I V and R R R V = I V and R I = Let’s come up with an equation for the current (I) that related to the Voltage (V) and Resistance (R): A large voltage (V) with a small resistance (R) results in a large current (I). I A small voltage (V) with a large resistance (R) results in a small current (I). I V R

  6. V I R I R This equation can be rearranged to form Ohm’s Law: Here are some graphs that represent the relationship:

  7. When we talk about electricity we often refer to the quantity power. Power is the rate at which energy is used. Units: (J/s =Watt) Let’s define power as it relates to an electrical circuit. The power is large when a large voltage (V) is used to produce a large current flow (I). Check out the units:

  8. The power equation can be combined with Ohm’s Law to give several variations in order calculate the power.

  9. Example 1: A 60W/120V light bulb is connected to a 120V power supply. What is the resistance of the light bulb and the current flowing in the circuit? The same 60W/120V light bulb is connected to a 240V power supply. What will be different from the calculations above? Since resistance is a property of the light bulb it will be the same as above, but the current and power of the bulb will be greater.

  10. Resistance of a wire R = Resistance (ohms Ω) ρ = resistivity (Ωm) depends of the material the wire is made from. A = cross sectional area (m2) A L

  11. Circuit Analysis Objective: TSW apply voltage, current and resistance to predict the behavior of various circuits by completing a VIP chart.

  12. R2 24V R1 R3 I Series Circuit • Current is the same. • Voltage is split. • When one bulb goes out, all go out • Greatest resistance is the brightest. • Rs=R1+R2+R3+...

  13. R2=5Ω 24V R3=4Ω Each resister represents a light bulb. Complete the VIP chart in order to rank the brightness of the bulbs. Series Circuit R1=3Ω

  14. R2=3Ω 12V R3=5Ω Each resister represents a light bulb. Complete the VIP chart in order to rank the brightness of the bulbs. Series Circuit R1=2Ω

  15. Each resister represents a light bulb. Complete the VIP chart in order to rank the brightness of the bulbs. Series Circuit R1=10Ω R2=8Ω 48V R3=12Ω

  16. R2 R1 R3 12V I1 I2 I3 I Parallel Circuit • Voltage is the same. • Current is split. • When one bulb goes out, others stay the same. • Least resistance is the brightest • 1/Rp=1/R1+1/R2+1/R3+ …

  17. R2=2Ω Each resister represents a light bulb. Complete the VIP chart in order to rank the brightness of the bulbs. Parallel Circuit R1=5Ω R3=10Ω 12V

  18. R2=8Ω R1=3Ω R3=4Ω 24V Each resister represents a light bulb. Complete the VIP chart in order to rank the brightness of the bulbs. Parallel Circuit

  19. R2=15Ω R1=10Ω R3=20Ω 50V Each resister represents a light bulb. Complete the VIP chart in order to rank the brightness of the bulbs. Parallel Circuit

  20. Combined Circuits • Map the currents. Currents divide at junctions • Find the total resistance. Start with resistors in series. • Resistors in series have the same current flowing through them. • Resistors in parallel have the same voltage (potential difference) • Use Ohm’s law to find the main current. • Use the loop rule to find the voltage (potential difference) across individual resistors. • Use proportional thinking to find the current flowing through individual resistors. • Complete the VIP chart. • Check: The power of individual resistors should always add to the power of the battery.

  21. R1=4Ω Each resister represents a light bulb. Complete the VIP chart in order to rank the brightness of the bulbs. R2=4Ω R3=4Ω 12V

  22. R1=4Ω Each resister represents a light bulb. Complete the VIP chart in order to rank the brightness of the bulbs. R3=3Ω 12V R2=2Ω

  23. R1=3Ω Each resister represents a light bulb. Complete the VIP chart in order to rank the brightness of the bulbs. R3=8Ω 15V R2=1Ω

  24. R1=2Ω Each resister represents a light bulb. Complete the VIP chart in order to rank the brightness of the bulbs. R2=3Ω R3=5Ω 24V

  25. R4=2Ω R2=3Ω R1=2Ω R3=1Ω Each resister represents a light bulb. Complete the VIP chart in order to rank the brightness of the bulbs. 28V

  26. R3=2Ω R1=4Ω R4=2Ω Each resister represents a light bulb. Complete the VIP chart in order to rank the brightness of the bulbs. 30V R2=6Ω

  27. 26V R5=6Ω R3=2Ω R2=3Ω R1=4Ω R4=1Ω Each resister represents a light bulb. Complete the VIP chart in order to rank the brightness of the bulbs.

  28. The circuit below has been connected for a long time such that all currents have reached their steady states. R1=1000Ω 30x10-6F 12V R2=500Ω Calculate the current in the 500Ω resistor. Calculate the charge stored in the capacitor. Calculate the power dissipated in the 1000Ω.

  29. Internal Resistance – The resistance due to the battery or power supply A battery consists of a EMF (ε) and an internal resistance. The potential difference across the terminals is called the terminal voltage. - + ri ε terminal voltage

  30. Example: The ammeter reads 0.5A. What is the emf of the battery? What is the terminal voltage across X and Y? 10Ω A X ε 14Ω internal resistance 2Ω Y

  31. Ammeters must be connected in series and ideally have zero resistance. R1 A ε R2

  32. Voltmeters must be connected in parallel and ideally have infinite resistance. R1 V ε R2

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