Lecture 13 feb14

# Lecture 13 feb14 - Phys240 Lecture 13 RC Circuits(end of ch...

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Lecture 13 RC Circuits (end of ch. 26) Time-dependent currents in circuits containing capacitors Begin Magnetism next week, ch. 27 Phys240

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Discharging a Capacitor (through a resistor) The capacitor is charged up to initial voltage V 0 =Q 0 /C, the switch is closed and current flows in discharging the capacitor i Question #1: At t=0 and t=∞ the charge on the capacitor is Q 0 and 0 respectively. What are the currents at t=0 and ∞? (t=0 is the instant AFTER closing switch) A. ∞ and 0 B. 0 and 0 C. Q 0 /RC and 0 D. 0 and Q 0 /RC E. Q 0 /RC and Q 0 /RC
Applying the loop rule…. (discharging) ) ( 1 0 0 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 - = 0 ) ( i Let’s 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 - - = = - = 0 0 ) ( Given the initial and final charge The current is then…… Both q and i decay exponentially with time constant = RC

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Discharging = decay down in q, i, and V C RC t RC t e R V e RC Q dt dq t i - - = = - = 0 0 ) ( (The text authors chose i in the opposite direction and hence the minus sign) RC t e Q t q - = 0 ) (
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