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

One Battery? Simplify! Resistors Capacitors Key formula: V=iR Q=CV In series: same current dQ/dt same charge Q Req=∑Rj 1/Ceq= ∑1/Cj In parallel: same voltage same voltage 1/Req= ∑1/Rj Ceq=∑Cj P = iV = i2R = V2/R U = QV/2 = Q2/2C = CV2

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

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. CE i(t) 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. C + - Solution: i(t) E/R

Too Many Batteries!

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.