Week 11 Day 1 Concept Question RC Circuit Correct Question At the instant the switch is closed Initially there is no change on the capacitor so it looks like a short Thus all the current will slow through it rather than through the bottom resistor Reference System for Circuit Analysis Simplify resistors in series and parallel Assign current and current direction in each branch Assign circulation direction for each loop Circulations direction across each element de nes before and after side of element De ne electric potential difference across a circuit element by V V a V b Sum of Potential Difference Around a Closed Path For each element choice of circulation direction de nes V V a V b Sum of potential differences across all elements around any closed circuit loop must be zero V E s 0 Current Conservation Sum of currents entering any junction in a circuit must equal sum of currents leaving that junction Sign Conventions Changed Capacitor and Current Assign Q and Q to each side of a capacitor When direction of current is toward the positive plate of a capacitor When direction of current is away from the positive plate of a capacitor Circulating across a capacitor from the negatively to positively charged plate increases the electric potential Circulating across a capacitor from the positively to negatively charged plate decreases the electric potential Sign Conventions Capacitor Capacitors in parallel Capacitors in series Capacitors in parallel have the same potential Capacitors in series split potential Concept Question Equivalent Capacitance Correct answer 2 Consider the circuit at right What is the equivalent capacitance Group Problem Charging a Capacitor Using the circuit rules determine the differential equation satis ed by the charge Q on the positive plate of the capacitor Your equation should establish a relationship between Q Q t R and Concept Question RC Circuit Power Capacitor Energy Balance Correct answer 1 An uncharged capacitor is connected to a battery resistor and switch The switch is initially open but at t 0 it is closed A very long time after the switch is closed the current in the circuit is nearly zero Circulating across a capacitor from the positive to negative plate decreases your potential If current ows in that direction the capacitor absorbs power stores charge Power delivered by a battery is equal to the power dissipated through the resistor plus the power absorbed by the capacitor At t the current through the capacitor will be zero At t the current through the lower resistor will be 2R Concept Question Current Thru Capacitor Correct answer 1 Concept Question Current Thru Capacitor Correct answer 1 Concept Question Open Switch in RC Circuit Correct answer Non Static Fields E is no longer a static eld After the switch has been closed for a very long time it is opened The current through the lower resistor doubles but stays in the same direction Non ideal Real Inductor Not only L but also some R In the direction of current Moving across an inductor in the direction of current contributes Moving across an inductor opposite the direction of current contributes Kirchhoff s Modi ed Second Rule Non Ideal Inductors Sign Conventions Inductor Group Problem RL Circuit For the circuit shown in the gure the currents through the two bottom branches as a function of time switch closes at t 0 opens at t T L R State the values of the current i just after switch is closed at t 0 ii just before the switch is opened at t T iii just after the switch is opened at t T
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