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PHYS 221 Recitation. Kevin Ralphs Week 4. Overview. HW Questions Current Resistance Resistivity Kirchhoff's Rules Capacitors, Current, Time. HW Questions. Ask Away…. Current. What does it tell me? The amount of charge flowing through a boundary The unit of measure is the ampere:
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PHYS 221 Recitation Kevin Ralphs Week 4
Overview • HW Questions • Current • Resistance • Resistivity • Kirchhoff's Rules • Capacitors, Current, Time
HW Questions Ask Away….
Current • What does it tell me? • The amount of charge flowing through a boundary • The unit of measure is the ampere: • The word “flow” implies there should be an equation similar to flux that describes this is the drift velocity. It is the average velocity of the charge carriers, is the charge density, is the number density (# of charge carriers/unit volume)
Resistance • What does it tell me? • The ratio of the potential drop in the “direction” of the current and the current in a segment and is measured in ohms () • Essentially it is telling you how tough it is to push charge through an object • Why do I care? • All things have resistance so it is critical to understand how it affects electric current • The resistor is another one of our linear electronic components • The potential difference across a resistor is given by Ohm’s Law ΔV: potential difference across a resistor, I: current passing through the resistor, R: resistor’s resistance, the sign depends on the direction of the current
Resistivity • The resistivity () tells us how easy it is to push charge through a material, regardless of its dimensions R: resistance, ρ: resistivity, L: length of resistor, A: cross-sectional area of resistor (assumes A is constant along the resistor’s length) • It has temperature dependence ρ: resistivity at temperature T, ρo: Resistivity at To =20°C
Kirchoff’s Rules • Loop Rule • Based on conservation of energy • Node Rule • Based on conservation of charge
Kirchhoff’s Rules General Procedure: • Choose loops so that every branch is covered by at least one loop • Choose current directions in each branch – this does not have to correspond to the direction of your loop • Write down each loop/node equation and solve using method of your choice. You need as many independent equations as you have currents to solve.
Kirchhoff’s Rules • The most common errors in applying Kirchhoff’s rules are sign errors Voltage Source Resistor (Black arrows denote a positive change in voltage; red negative) Current
Capacitors, Current, Time • You will be responsible for understanding how a capacitor behaves at various times during charging/discharging • The end points are simple • If uncharged, a capacitor acts as a short • If charged, a capacitor acts as an open • The words “after a long time” or similar mean it has gone from charged to uncharged or vice versa
Capacitors, Current, Time • In between it is governed by equations • Note: vary depending on whether you are charging/discharging and what resistors you are charging/discharging through