Lecture+13+feb16+ctools

Lecture+13+feb16+ctools - Lecture 13 RC Circuits (end of...

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Unformatted text preview: Lecture 13 RC Circuits (end of ch. 26) Time-dependent currents in circuits containing capacitors Begin Magnetism Next Week Discharging a Capacitor (through a resistor) The capacitor is charged up to initial voltage V =Q /C, the switch is closed and current flows in discharging the capacitor i Question : At t=0 and t= the charge on the capacitor is Q and 0 respectively. What are the currents at t=0 and ? Applying the loop rule. (discharging) ) ( 1 t q RC dt dq dt dq R c q iR C q- = = + =- B Ae t q RC t + =- ) ( RC t e Q t q- = ) ( i Lets go clockwise around, starting at point c. (Note: here we should set i = -dq/dt because i is reducing the charge on the capacitor) RC t RC t e R V e RC Q dt dq t i-- = =- = ) ( Given the initial and final charge The current is then Both q and i decay exponentially with time constant = RC Discharging = decay down in q, i, and V C RC t RC t e R V e RC Q dt dq t i-- = =- = ) ( (The text authors chose i in the opposite direction and hence the minus sign) RC t e Q t q- = ) ( Charging a Capacitor...
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This note was uploaded on 02/15/2012 for the course PHYS 240 taught by Professor Winn during the Winter '11 term at University of Michigan.

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Lecture+13+feb16+ctools - Lecture 13 RC Circuits (end of...

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