PHY 184 Week 7
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This 4 page Class Notes was uploaded by Cameron Blochwitz on Sunday October 16, 2016. The Class Notes belongs to PHY 184 at Michigan State University taught by Oscar Naviliat Cuncic in Fall 2016. Since its upload, it has received 2 views. For similar materials see Physics for Scientists and Engineers II in Physics at Michigan State University.
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Date Created: 10/16/16
PHY 184 Week 7 Notes-DC Circuits 10/10-10/13 Most practical circuits cannon be resolved into series or parallel systems of capacitors and resistors o To handle this we use Kirchhoff’s rules A Junction is a place where 3+ wires connect o Each connection between 2 junctions is called a branch Each branch has the same current within the branch A Loop in a current is any set of connected wires forming a closed path o You can get back to where you started Kirchhoff’s Junction Rule The sum of currents entering a junction equals the sum of currents leaving the junction Positive terms enter, negative terms exit n i =0 o k=1k Consider a Junction with current i e1tering and i an2 i lea3ing i =i +i o 1 2 3 This is a direct result of conservation of electric charge o Junctions cannot store charge Kirchhoff’s Loop Rule The potential difference of a complete loop is equal to 0 o Direction is irrelevant All that matter is that you follow the same conventions around the loop Resistors o Along Current -iR o Opposite Current +iR Battery o Same as emf +V o Opposite emf -V Emf goes from negative to positive The direction you travel around the loop and the direction of the current are totally arbitrary o Will not change final result outside of a minus sign General Observations Voltage drop is a linear relation Kirchhoff’s Junction Rule established linear relations between currents in the junctions o Coefficients are +1 or -1 If a circuit contains only batteries and resistors Kirchhoff’s Loop Rule established other linear relations For Linear circuits we can determine the voltage by knowing the current in each branch A circuit with n junction has n-1 independent equations A circuit with 4 junctions and three loops have 3 equations from junctions and 3 from loops o Choose the smallest loops to work on Analysis of Linear Circuits Choose a direction for all currents Choose loops and a way to travel them Write the n-1 relations for currents Look at ΔV along the selected loops and write the loop and write the loop rule Finally, you have N equations and N unknowns o You can solve the equation Devices Ammeter measures current o Is in series and has low resistance A Voltmeter Measures Voltage o Is in parallel and has high resistance RC Circuits An RC circuit has both a resistor and a capacitor o They will vary over time Charging a Capacitor We start with the capacitor uncharged When the switch is closed current begins to flow building the charge on the capacitor o This creates a potential difference in the capacitor When the capacitor is fully charged no current will flow o Potential from the capacitor and the battery are equal When charged the charge on the plates is q=CV To Calculate the current in the circuit we use the KLR for a single loop Start at a given point with arbitrary current and loop directions Applying KLR V−i t)R− q(t=0 o C By definition dq(t) o (t= dt So we can rewrite KLR as V− dq(t− q(t=0 o dt C Which can be rearranged to dq(t) 1 q o ( ) = − ( ) () dt R c Integrating this and solving for q gives −t o qt)=qmax(1−eRC)¿ o τ=RC qmaxCV o Current flowing though the circuit is the time derivative −t (t= V eRC o r i0= V R Potential difference across a capacitor can be written RC o V t)=V (1−e ) Discharging a Capacitor Consider the circuit containing one resistor and one capacitor o When disconnected from a battery the charged capacitor will begin to discharge until depleted Vr+V i0 q(t) (t)R+ C =0 Solution is therefo−t RC o q(t=q 0 Current is q o it)= RC
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