DC circuits Physics 114 11/23/2018 Lecture VI

Test problem For resistors connected in series, which of the following will be the same for each of the resistors? A The current through. B The potential difference across. C The resistance of. D The power dissipated by. 11/23/2018 Lecture VI

Test problem For resistors connected in parallel, which of the following will be the same for each of the resistors? A The current through. B The potential difference across. C The resistance of. D The power dissipated by. 11/23/2018 Lecture VI

Electric battery For idealized battery emf – supplied voltage Real life batteries have internal resistance r Terminal voltage (supplied to the circuit) Vab=emf-Ir 11/23/2018 Lecture VI

Series vs parallel - Req R1=R2R R2=R3=R Req=3R4R R1=R2R R2=R3=R Req=R/3=2R/62R/5 If any of R’s increased the equivalent resistance will increase in both parallel and series connection. 11/23/2018 Lecture VI

Series vs parallel - I R1=R2R R2=R3=R Req=3R4R I=V/Req=V/3RV/4R I1=I2=I3=I R1=R2R R2=R3=R Req=R/3=2R/62R/5 I=V/Req=6V/2R5V/2R I1=V/R1=V/RV/2R I2=I3=V/R – the same 11/23/2018 Lecture VI

Kirchhoff’s rules Junction rule (charge conservation): At any junction point the sum of all current entering the junction must equal the sum of all currents leaving the junction Do not disregard signs! Assign initial signs based on your best guess – if you were wrong the currents will turn to be negative (opposite to initial guess) Loop rule (energy conservation): The sum of the changes in potential around any closed path of a circuit must be zero. Choose a direction in which you circle the loop (random) For resistor Vab=-IR – negative if current along the loop direction For resistor Vab=+IR – positive if current opposite the loop direction For battery Vab – positive if the direction is from – to + For resistor Vab –negative if the direction is from + to - 11/23/2018 Lecture VI

Kirchhoff’s rules Loop rule (energy conservation): The sum of the changes in potential around any closed path of a circuit must be zero. Choose a direction in which you circle the loop (random) For resistor Vab=-IR – negative if current along the loop direction For resistor Vab=+IR – positive if current opposite the loop direction For battery Vab – positive if the direction is from – to + For resistor Vab –negative if the direction is from + to - 11/23/2018 Lecture VI

Capacitor connections No DC current through capacitor, Just store charge. Parallel connection: Same voltage – V1=V2=V3=V Different charges: Q1=C1V Q2=C2V Q3=C3V Q=Q1+Q2+Q3=V(C1+C2+C3) Ceq=C1+C2+C3 Series connection: Same charge (QA=0  -Q1+Q2=0) Different voltages V=V1+V2+V3 11/23/2018 Lecture VI

Safety and grounding Voltage does not kill. Current kills 1mA – “feel” 10mA – muscle contraction 70 mA – “ventricular fibrillation” ~1A – hearts stops (not as harmful) >10A – “fry” Usually V is fixed To reduce I – increase R Dry surface Insulating sole Insulating floor To avoid high V - Ground the case (3prong plug) 11/23/2018 Lecture VI