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##### CHAPTER-27

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**CHAPTER-27**Circuits**Ch 27-2 Pumping Charges**• Charge Pump: • A emf device that maintains steady flow of charges through the resistor. • Emf device does work on charge carrier by doing work • Within the emf device , positive charge carrier moves from negative terminal (a region of low electric potential energy) to positive terminal (a region of high electric potential energy) against E field inside the device. • This energy , which is chemical energy , is supplied by emf device • =amount of work dW/charge dq**Ch 27-3 Work, Energy, and Emf**• Circuit containing two batteries • For a circuit with two emf with similar terminal connected net emf in the circuit is difference of the two emf and net current direction in the direction of the stronger emf. • For a circuit with two emf with opposite terminal connected net emf in the circuit is sum of the two emf and net current direction in the direction of the any of the emf.**Ch 27-4 Calculating the Current in a Single-Loop Circuit**• Energy Method • A current i passes through the resistor R for a time dt sec. Charge dq=idt passes through the resistor. • Work done by battery to move this charge through the resistor dW=dq= idt • His work must be equal to thermal energy dissipated in the resistor idt=i2Rdt • =iR and i= /R • Potential Method • Potential method involve calculating the potential difference between two points V=Vf-Vi when you move in a circuit • If you move in a circuit clockwise or anticlockwise in a loop the Vi=Vf • V=0**Ch 27-4 Calculating the Current in a Single-Loop Circuit**• Kirchoff’s Loop Rule • Algebric sum of potential drop V encountered in a complete traversal of any loop is zero i.e For a loop Vi=0 • Resistance Rule • For a move through the resistance R along direction of current i potential drop V= -iR • For a move through resistance R in direction opposite to current i potential drop V= +iR • EMF Rule: • For a move through emf device along direction of emf arrow potential drop V= + • For a move through emf device opposite to direction of emf arrow potential drop V= -**Ch 27-4 Calculating the Current in a Single-Loop Circuit**• Potential Method • Moving in the circuit clock wise from point a • V= -iR=0 • = iR and i= /R**Ch 27-5 Other Single-Loop Circuit**• Battery Internal Resistance: • Electrical resistance of the battery conducting material , shown with resistance r in series with emf • Resistance in Series: Resistance in series can be represented by an equivalent resistance Req given by : Req = Ri**Ch 27-6 Potential Difference between two points**• To find potential difference between any two points in a circuit, start at one point and traverse the circuit to the other point , following any path and add algebraically the changes in potential you encounter • To calculate potential difference Vb-Va start at a then • Va+ -ir =Vb then • Vb-Va= V= -ir A current I through a circuit containing a battery with internal resistance r and an external resistor R is i=/(r+R) • Vb-Va= V= -ir = -r/(r+R)= R/(R+r)**Ch 27-6 Potential Difference between two points**• Grounding a Circuit: • Connecting the circuit to a conducting path to Earth. The potential at the grounding point is defined to be Zero. • Power, potential and Emf • When a emf device does work to establish a current i in the circuit, the device transfers its chemical energy to the charge carrier. It loses power in its internal resistance r. • Energy transfer rate P from emf to charge carrier • P= iV=i(-ir)=i-i2r • Pr=i2r (internal dissipation rate) • Pemf= i**Ch 27-7 Multiloop Circuits**Junction rule: The sum of currents entering the junction must be equal to the currents leaving the junction Resistance in Parallel: • The resistance connected in parallelhave common voltage • Resistance in parallel can be represented by an equivalent resistance Req given by : • 1/Req =1/ Ri**Ch 27-8 Ammeter and Voltmeter**• Ameter A connected in series while voltmeter V is used in Paralell. • If RA is internal resistance of an ammeter and RV is internal resistance of a voltmeter then : • RA should be very small • RV should be very large**Ch 27-9 RC Circuits**• Charging the capacitor-time varying current • In switch position a current flows through the resistor R and charge q start building up on the capacitor plate. The capacitor voltage V= q/C. • For fully charged capacitor no current flows through the resistor and voltage V across the capacitor is then q=C. • During charging process the loop rule to the circuit gives: • - iR-q/C=0 ; = Rdq/dt+q/C • q=C(1-e-t/RC) • Current i=dq/dt= (/R) e-t/RC • Voltage V=q/c=(1-e-t/RC) • Time constant =RC • q=C(1-e-t/RC)=C(1-e-1)=0.63 C**Ch 27-9 RC Circuits**• Discharging a capacitor • In switch position b the charging equation • = Rdq/dt+q/C reduces to • 0 = Rdq/dt+q/C ( = 0) • Then q=q0e-t/RC and q0=CV0 • i=dq/dt=-(q0/RC)e-t/RC=-i0e-t/RC