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Lesson 6 Direct Current Circuits Electro Motive Force Internal Resistance Lesson 6 and Parallel Resistors in Series Kirchoffs Rules Topics RC Circuits Charging Discharging Capacitors Electrical Instruments Galvanometer Ammeter Voltmeter Wheatstone Bridge Potentiometer Electro Motive Force (emf) EMF I 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 II EMF Work Done per unit charge by electrical pump e dW = dQ Charge Pump Current flowing internally in battery feels resistance Internal resistance, r Flowing positive charges (current) experience drop of electric potential in resistor V=IR + R - Charge Pump Internal Resistance - - + + - + Terminals Terminal Potential Difference V = E - Ir Picture e Ir V = = IR Power Vand Internal = IR Ir e Resistance e I= Rr Thus power generated by emf e I = e 2 Rr Combinations of Combination of Resistors 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 V = V 1 V 2 = IR1 IR2 Series V = I R1 R2 = IReq Req = i Ri V R1 1 1 I = V = R2 R1 1 1 1 = Req R1 R2 I = I1 I2 = Parallel 1 = Req i 1 Ri V R2 V Req 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 Kirchoffs Rules II The Sum of the Potential Differences around a closed circuit loop must be zero Conservation of Energy Picture RC Circuits Non Steady State Non Equilibrium Current varies with time RC circuits Picture Charging I When switch is closed q e IR = 0 C Thus at time t = 0, q 0 = 0 I0 e = I 0 = R When capacitor is fully charged the current in the circuit is zero and the charge on the capacitor is a max Q = qmax = Ce e d dt e IR IR q C = 0 q dI = 0 = 0 R C dt dI I R = 0 dt C dI 1 = dt I RC Charging II I dI I I = 1 RC 0 I t = ln I 0 RC I t = R e t RC 1 C dq dt t dt 0 I t = I 0e e t RC I t = e e R t RC Charging III e dq = dt R e dq = q dq = R q t = C e R e e e 0 1 e t RC t RC t RC dt t e t RC dt 0 = Q 1 e t RC Time Constant Time Constant = RC V Q Q = RC = = Q = s I V s Discharging Discharging I +Q -Q q = IR from Kirchoff C dq = I the rate of decrease of charge dq q R = dt C dq 1 = dt q RC Discharging II q Q dq 1 = q RC t dt 0 q t ln = Q RC qt = Qe dq Q I t = = e dt RC t RC t RC = I0 e t RC