Physics 2112 Unit 8: CapacitorsToday’s Concept: Capacitors in a circuits Dielectrics power in capacitorsUnit 8, on slide 1Where us are…….Unit 8, on slide 2Simple Capacitor Circuit QVDirection that arrows is the contrary of the direction the electron motionVCCSorry. That historical. There is naught I can do.Q = VCQ This “Q” really means that the battery has actually moved charge Q indigenous one plate to the other, so the one plate holds +Q and also the various other -Q.Electricity & Magnetism lecture 8, on slide 3Parallel Capacitor Circuit QtotalVC2C1 Q1 = C1VQ2 = C2VQtotalKey point: V is the exact same for both capacitors an essential Point: Qtotal = Q1 + Q2 = VC1 + VC2 = V(C1 + C2) Ctotal = C1 + C2 electrical power & Magnetism great 8, slide 4Series Capacitor Circuit Q = VCtotalQC1V1VQVC2 V2Q vital point: Q is the very same for both capacitors key point: Q = VCtotal = V1C1 = V2C2Also: V = V1 + V2Q/Ctotal = Q/C1 + Q/C2 1 1 1 = + C2 Ctotal C1 power & Magnetism lecture 8, slide 5Capacitor review SeriesParallel C1C1WiringVoltage CurrentC2Every electron the goes v one should go through the other different for every capacitor. Vtotal = V1 + V2 same for each capacitor Itotal = I1 = I2Decreases Capacitance 1/C = 1/C + 1/C eq 1 2C2 every resistor ~ above a different wire. Exact same for each capacitor. Vtotal = V1 = V2 various for every capacitor Itotal = I1 + I2Increases Ceq = C1 + C2 electrical power & Magnetism great 9, slide 6Example 8.1 (Capacitors in Series) offered the circuit come the left: C1 =3uFV =12VC2 =9uFWhat is Q1? What is V1? theoretical Idea:CV = Q Plan: • • •Find indistinguishable capacitance Use understanding that in series Q1 = Q2 = Qtot find V using Q = CVUnit 8, slide 7Example 8.2 (Capacitors in Parallel) offered the circuit come the left: C2 =9uFV =12VC1 =3uFWhat is Q1? What is Q2? theoretical Idea:CV = Q Plan: • • •Find tantamount capacitance Use knowledge that in parallel V1 = V2 uncover Q making use of Q = CVUnit 8, slide 8CheckPoint: 3 Capacitor configurations The three configurations shown listed below are constructed using similar capacitors. Which of this configurations has actually lowest complete capacitance? C B A C CCC CCtotal = C1/Ctotal = 1/C + 1/CCtotal = 2C= 2/C Ctotal = C/2Electricity & Magnetism great 8, slide 9CheckPoint: two Capacitor configurations The 2 configurations shown listed below are built using similar capacitors. I beg your pardon of this configurations has actually the lowest overall capacitance? BACCCCCCleft = C/2 Ctotal = CA. B. C.Cright = C/2Ctotal = cleft + Cright C=Ctotal A B Both configurations have the same capacitance electricity & Magnetism great 8, slide 10CheckPoint: Capacitor Network A circuit consists of three unequal capacitors C1, C2, and also C3 which are connected to a battery of voltage V0. The capacitance of C2 is double that of C1. The capacitance the C3 is 3 times that of C1. The capacitors achieve charges Q1, Q2, and also Q3. Q2C2Compare Q1, Q2, and also Q3. A. Q1 > Q3 > Q2 V0 B. Q1 > Q2 > Q3 C. Q1 > Q2 = Q3 D. Q1 = Q2 = Q3 E. Q1 V2C1 V1Q1V3C3Q3Unit 8, slide 11Example 8.3 (Capacitor Network) C3 =12uFGiven the circuit to the left: C1 =3uFC2 =11uFWhat is Q1?V =12CWhat is Q3? C5 =9uFC4 =6uF theoretical Idea:CV = QFind V at every capacitor and also then Q . Plan: • • • •Break circuit down into elements that space in parrallel or in series. Uncover equivalent capacitance work backwards to discover DV across each one good Q utilizing Q = CV Unit 8, slide 12Example 8.1 (Capacitor Network) C3C4 C3C5C1234C2C1C2C1C34C5C12345C5 Unit 8, slide 13Energy in a Capacitor In Prelecture 7 us calculated the work done to relocate charge Q native one plate to another:C+QV -QU = 1/2QV = 1/2CV2 = 1/2Q2/CSince Q = VCThis is potential energy waiting to be used…Electricity & Magnetism great 8, on slide 14Messing with Capacitors If connected to a battery V stays consistent V1 = V VC1 = k CQ1 = C1V1 = k CV = k QIf isolated then complete Q stays consistent Q1 = QC1 = k CV1 = Q1/C1 = Q/k C = V /k electrical energy & Magnetism class 8, slide 15DielectricsC1 = k C0C0 VQ0 = VC0Q1 = VC1VBy adding a dielectric girlfriend are simply making a new capacitor with larger capacitance (factor the k)Electricity & Magnetism lecture 8, slide 16CheckPoint: Capacitors and Dielectrics 1 Two identical parallel key capacitors are given the same charge Q, after which they room disconnected from the battery. After ~ C2 has actually been charged and disconnected, the is filled v a dielectric. To compare the voltages the the 2 capacitors. A. V1 > V2 B. V1 = V2 C. V1 electrical energy & Magnetism class 8, on slide 17CheckPoint: Capacitors and also Dielectrics 2Two identical parallel key capacitors are provided the exact same charge Q, after i beg your pardon they are disconnected native the battery. After ~ C2 has actually been charged and disconnected, it is filled through a dielectric. To compare the potential power stored through the two capacitors. A. U1 > U2 B. U1 = U2 C. U1 power & Magnetism great 8, slide 18CheckPoint: Capacitors and Dielectrics 3 The 2 capacitors are now linked to each various other by wires as shown. How will the charge redistribute itself, if in ~ all? A. The charges will circulation so that the fee on C1 will become equal to the fee on C2. B. The dues will flow so that the energy stored in C1 will become equal to the power stored in C2 C. The fees will circulation so the the potential difference throughout C1 will end up being the exact same as the potential difference across C2. D. No charges will certainly flow.
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The charge on the capacitors will remain what that was before they to be connected. Power & Magnetism class 8, slide 19Example 8.4 (Partial Dielectric) C0Vx0VAn air-gap capacitor, having capacitance k C0 and also width x0 is connected to a x0/4 battery of voltage V.A dielectric (k ) of width x0/4 is put into the gap as shown.What is Qf, the last charge on the capacitor? conceptual Analysis: CQ VStrategic Analysis: Think of brand-new capacitor as two capacitors in parallel Calculate brand-new capacitance C Apply an interpretation of capacitance to recognize Q electricity & Magnetism great 8, on slide 20CalculationkkA1 =3/4 AoA2 =1/4 AoElectricity & Magnetism lecture 8, slide 21