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Understanding Electric Current, Circuits, and Ohm's Law

Learn about electric current, circuits, resistance, Ohm's Law, temperature variation, electrical energy, and power in this comprehensive lecture.

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Understanding Electric Current, Circuits, and Ohm's Law

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  1. Lecture 7 • Electric Current • Circuits • Resistance and Ohms law • Temperature variation • Electrical energy

  2. Resistance • In a conductor, the voltage applied across the ends of the conductor is proportional to the current through the conductor • The constant of proportionality is the resistance of the conductor

  3. Fig. 17-CO, p.568

  4. Resistance, cont • Units of resistance are ohms (Ω) • 1 Ω = 1 V / A • Resistance in a circuit arises due to collisions between the electrons carrying the current with the fixed atoms inside the conductor

  5. Georg Simon Ohm • 1787 – 1854 • Formulated the concept of resistance • Discovered the proportionality between current and voltages

  6. Ohm’s Law • Experiments show that for many materials, including most metals, the resistance remains constant over a wide range of applied voltages or currents • This statement has become known as Ohm’s Law • ΔV = I R • Ohm’s Law is an empirical relationship that is valid only for certain materials • Materials that obey Ohm’s Law are said to be ohmic

  7. Ohm’s Law, cont • An ohmic device • The resistance is constant over a wide range of voltages • The relationship between current and voltage is linear • The slope is related to the resistance • Demo 2

  8. Ohm’s Law, final • Non-ohmic materials are those whose resistance changes with voltage or current • The current-voltage relationship is nonlinear • A diode is a common example of a non-ohmic device

  9. Resistivity • The resistance of an ohmic conductor is proportional to its length, L, and inversely proportional to its cross-sectional area, A • ρ is the constant of proportionality and is called the resistivity of the material

  10. Table 17-1, p.576

  11. Temperature Variation of Resistivity • For most metals, resistivity increases with increasing temperature • With a higher temperature, the metal’s constituent atoms vibrate with increasing amplitude • The electrons find it more difficult to pass through the atoms

  12. Temperature Variation of Resistivity, cont • For most metals, resistivity increases approximately linearly with temperature over a limited temperature range • ρ is the resistivity at some temperature T • ρo is the resistivity at some reference temperature To • To is usually taken to be 20° C = 68 ° F •  is the temperature coefficient of resistivity

  13. Temperature Variation of Resistance • Since the resistance of a conductor with uniform cross sectional area is proportional to the resistivity, you can find the effect of temperature on resistance

  14. Superconductors • A class of materials and compounds whose resistances fall to virtually zero below a certain temperature, TC • TC is called the critical temperature • The graph is the same as a normal metal above TC, but suddenly drops to zero at TC

  15. Superconductors, cont • The value of TC is sensitive to • Chemical composition • Pressure • Crystalline structure • Once a current is set up in a superconductor, it persists without any applied voltage • Since R = 0

  16. Superconductor Timeline • 1911 • Superconductivity discovered by H. Kamerlingh Onnes • 1986 • High temperature superconductivity discovered by Bednorz and Müller • Superconductivity near 30 K • 1987 • Superconductivity at 96 K and 105 K • Current • More materials and more applications

  17. Table 17-2, p.579

  18. Superconductor, final • Good conductors do not necessarily exhibit superconductivity • One application is superconducting magnets

  19. Electrical Energy and Power • In a circuit, as a charge moves through the battery, the electrical potential energy of the system is increased by ΔQΔV • The chemical potential energy of the battery decreases by the same amount • As the charge moves through a resistor, it loses this potential energy during collisions with atoms in the resistor • The temperature of the resistor will increase

  20. Energy Transfer in the Circuit • Consider the circuit shown • Imagine a quantity of positive charge, DQ, moving around the circuit from point A back to point A

  21. Energy Transfer in the Circuit, cont • Point A is the reference point • It is grounded and its potential is taken to be zero • As the charge moves through the battery from A to B, the potential energy of the system increases by DQDV • The chemical energy of the battery decreases by the same amount

  22. Energy Transfer in the Circuit, final • As the charge moves through the resistor, from C to D, it loses energy in collisions with the atoms of the resistor • The energy is transferred to internal energy • When the charge returns to A, the net result is that some chemical energy of the battery has been delivered to the resistor and caused its temperature to rise

  23. Electrical Energy and Power, cont • The rate at which the energy is lost is the power • From Ohm’s Law, alternate forms of power are

  24. Electrical Energy and Power, final • The SI unit of power is Watt (W) • I must be in Amperes, R in ohms and DV in Volts • The unit of energy used by electric companies is the kilowatt-hour • This is defined in terms of the unit of power and the amount of time it is supplied • 1 kWh = 3.60 x 106 J

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