Lesson 6 Direct Current Circuits  Electro Motive Force  Internal Resistance  Resistors in Series and Parallel  Kirchoffs Rules

 RC Circuits  Charging  Discharging Capacitors  Electrical Instruments  Galvanometer  Ammeter  Voltmeter  Wheatstone Bridge  Potentiometer Topics

Electro Motive Force (emf) Source of emf is any device that increases the potential energy of charges circulating in a circuit. Electric Potential increases by the emf E as charge goes from negative to positive plate of battery. EMF I

EMF is Work Done per unit charge by electrical pump   dW dQ EMF II

 Battery is a Charge Pump  Current flowing internally in battery feels a resistance this is an  Internal resistance, r  Flowing positive charges (current) experience drop of electric potential in resistor - V=IR R + Charge Pump

Terminals  Terminal Potential Difference  V = E - Ir + - Internal Resistance

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Power and Internal Resistance

Combination of Resistors Combinations of Resistors  Parallel  same electric potential felt by each element  Series  electric potential felt by the combination is the sum of the potentials across each element

Series

Parallel

Kirchoff’s Rules The sum of the currents entering a junction must equal the sum of the currents leaving Conservation of Charge Kirchoffs Rules I

The Sum of the Potential Differences around a closed circuit loop must be zero Conservation of Energy Kirchoffs Rules II

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RC circuits RC Circuits  Non Steady State  Non Equilibrium  Current varies with time

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Charging I

Charging II   IR  q C  0 d dt   IR  q C        0  0  R dI dt  1 C dq dt  R dI dt  I C  0  dI I  1 RC dt  dI I I 0 I   1 RC dt 0 t   ln I I 0       t RC  It   I 0 e  t It    R e  t

Charging III It    R e  t RC dq dt   R e  t RC  dq   R e  t RC dt dq 0 q    R e  t RC dt 0 t   qt   C  1  e  t RC          Q1  e  t        

Time Constant

Discharging +Q -Q-Q IR  q C from Kirchoff I  dq dt the rate of decrease of charge Discharging I

Discharging II