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DC Circuit Connections

Master the concepts of parallel and series connections in DC circuits, including RC circuits, charge conservation, Ohm's law, and energy conservation. Learn how to rearrange circuits and differentiate between series and parallel connections for enhanced problem-solving skills.

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DC Circuit Connections

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  1. DC circuits Physics 122 Lecture X

  2. Skills • Solve problems on parallel and series connections in DC circuits • RC circuits Lecture X

  3. Symbols • Circuits can be rearranged: • Wires with negligible resistance can be • Stretched • Bended • Collapsed to a point Lecture X

  4. Skiing  electric circuit a Cannot stop at b, must get to c – ski lift: V=V1+V2- Net voltage drop in a circuit is always equal to the supplied voltage (e.g. battery) b Ski lift c Battery Lecture X

  5. Series connection • Charge conservation: • I=I1=I2=I3 • Ohm’s law • V1=IR1; V2=IR2; V3=IR3 • Energy conservation: • qV=qV1+qV2+qV3 • V=V1+V2+V3 • IReq=IR1+IR2+IR3 • Req=R1+R2+R3 Lecture X

  6. Parallel connection • Charge conservation:I=I1+I2+I3 • Energy conservation: V=V1=V2=V3 • Ohm’s law: I1=V/R1; I2=V/R2; I3=V/R3 Lecture X

  7. R1=R2=R3=R Req=3R R1=R2=R3=R Req=R/3 Series vs parallel - Req > Equivalent resistance is larger in series connection. Lecture X

  8. R1=R2=R3=R Req=3R I=V/(3R) I1=I2=I3=I=V/(3R) R1=R2=R3=R Req=R/3 I=3V/R I1=I2=I3=I/3=V/R Series vs parallel - I < < Total current and individual currents are smaller in series connection. Lecture X

  9. R1=R2=R3=R Req=3R I=V/3R  Pnet=V2/3R I1=V/3R P1=V2/9R R1=R2=R3=R Req=R/3 I=3V/R  Pnet=3V2/R I1=V/R  P1=V2/R Series vs parallel - P P1=I2R Pnet=IV Brightness proportional to power < < Total and individual power consumptions are smaller in series connection. Light bulbs are brighter in parallel connection. Lecture X

  10. DC circuits • Series connection • I=I1=I2=I3 • V=V1+V2+V3 • Req=R1+R2+R3 • Parallel connection • I=I1+I2+I3 • V=V1=V2=V3 Lecture X

  11. 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 Lecture X

  12. 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) Lecture X

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

  14. 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 Series vs parallel - I Lecture X

  15. 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. Lecture X

  16. 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. Lecture X

  17. RC circuit • RC circuit contains at least one capacitor (C ) and at least one resistor (R ). +Q C -Q Lecture X

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