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Understanding DC Circuit Simplification: Resistors, Capacitors, and Key Formulas

Learn about DC circuits, simplification techniques, capacitor charging and discharging, time constants, and safety practices for handling batteries. Understand the fundamentals of current, voltage, and resistance in circuit components.

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Understanding DC Circuit Simplification: Resistors, Capacitors, and Key Formulas

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  1. Physics 2113 Jonathan Dowling Lecture 24: FRI 13 MAR DC circuits III Ch27.4-9

  2. One Battery? Simplify! ResistorsCapacitors Key formula: V=iRQ=CV In series: same current dQ/dtsame charge Q Req=∑Rj1/Ceq=∑1/Cj In parallel: same voltagesame voltage 1/Req=∑1/RjCeq=∑Cj P = iV = i2R = V2/R U = QV/2 = Q2/2C = CV2

  3. Many Batteries? Loop & Junction! Three Batteries: Straight to Loop & Junction One Battery: Simplify First

  4. i(t) CE E/R RC Circuits: Charging a Capacitor In these circuits, current will change for a while, and then stay constant. We want to solve for current as a function of time i(t)=dq/dt. The charge on the capacitor will also be a function of time: q(t). The voltage across the resistor and the capacitor also change with time. To charge the capacitor, close the switch on a. VC=Q/C VR=iR A differential equation for q(t)! The solution is: Time constant: τ = RC Time i drops to 1/e.

  5. Solution: i(t) + C E/R - RC Circuits: Discharging a Capacitor Assume the switch has been closed on a for a long time: the capacitor will be charged with Q=CE. +++ --- Then, close the switch on b: charges find their way across the circuit, establishing a current.

  6. Too Many Batteries!

  7. Fire Hazard: Filling gas can in pickup truck with plastic bed liner. • Safe Practice: Always place gas can on ground before refueling. • Touch can with gas dispenser nozzle before removing can lid. • Keep gas dispenser nozzle in contact with can inlet when filling.

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