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Join Prof. Reitze for this week’s Ch. 17 lectures covering current, resistance, and problems. WebAssign HW due Friday. Exam 1 on Feb. 16, 8:20–10:10 pm. See room assignments and ask questions if needed.
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Announcements • Prof. Reitze will be giving this week’s lectures on Ch. 17 • Chapter 17 covers current and resistance • WebAssign HW Set 4 due this Friday • Problems cover material from Chapters 17 • Exam 1 is coming! 8:20 – 10:10 pm Wednesday, February 16 • Room assignments: • QUESTIONS? PLEASE ASK!
Current • Current = rate at which the charge flows through a surface in a material • The SI unit of current is Ampere (A); 1 A = 1 C/s • Instantaneous current: • Direction (convention) - the direction positive charge would flow • But, in most materials the electrons carry the current
Example Problem 17.3 In the Bohr model of the hydrogen atom, an electron in the lowest energy state moves at a speed of 2.19 x 106 m/s in a circular path having a radius of 5.29 x 10-11 m. What is the effective current associated with the orbiting electron?
Current and Drift Speed • n charge carriers per unit volume with unit charge q moving through a volume A Δx • Total charge DQ is DQ = n A Dx q = n A vdDt q • Rewrite in terms of current as I = n A vd q • No E field present: charges move randomly • E field present: charges ‘drift’ preferentially in a direction producing current
Example Problem • 17.8 An aluminum wire carrying a current of 5.0 A has a cross-sectional area of 4.0 x 10-6 m2. Find the drift speed of the electrons in the wire.
Measuring current and voltage in a circuit • An ammeter is used to measure current • In series with the bulb • A voltmeter is used to measure voltage (potential difference) • In parallel with the bulb
Resistance • 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 • 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
Ohm’s Law Ohmic • For many materials, including most metals, 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 Non-ohmic
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
Example Problem • 17.12 Suppose you wish to fabricate a uniform wire out of 1 g of copper. If the wire is to have a resistance R = 0.50 W, and if all of the copper wire is to be used,what will be the (a) length and (b) diameter of the wire?
