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RC Circuits Physics 102 Professor Lee Carkner Lecture 16 Series and Parallel + - I1 DV = 6 V I2 6W I3 6W 10 W 4W DV = 6 for each branch so I2 = DV/R = 6/6 = 1 A and I3 = DV/R = 6/10 = 0.6 A Equivalent resistance total: 1/Req = 1/6 +1/10, Req = 3.75 W, so I1 = Ieq = DV/Req = 6/3.75 = 1.6 A through battery (DV=6) Kirchhoff’s Rules + - I1 DV = 6 V I2 6W I3 6W 4W Left loop: 6 - 6I2 = 0 Right loop: 6I2 - 6I3 - 4I3 = 0 I1 = I2 +I3 Voltage: For battery DV = 6 V, for 6W, DV = 6I2 = 6 V, for 2nd 6W, DV = 6I3 = 3.6 V, for 4W, DV = 4I3 = 2.4V Kirchhoff Tips Find the currents Each single branch has a current Indicate current direction Apply junction rule Currents in equal currents out More Kirchhoff Tips Apply the loop rule Sum of all DV equal to zero From - to + terminal the DV is equal to +e Moving with the current the DV is - IR Solve equations Need as many equations as unknowns Check your work Today’s PAL Use Kichhoff’s rules to find the current through each resistor Capacitance The value of C depends on its physical properties: C = ke0A/d How can we combine capacitors in circuits? Simple Circuit C - + Battery (DV) connected to capacitor (C) Q + DV The capacitor experiences potential difference of DV and has stored charge of Q = C DV Capacitors in Parallel C1 Potential difference across each is the same (DV) C2 But: Q2 = C2DV The equivalent capacitance is: + DV Ceq = C1 + C2 Capacitors in Series C1 + - + C2 - Charge stored by each is the same (Q) Equivalent capacitor also has a charge of Q Since DV = Q/C: The equivalent capacitance is: + DV 1/Ceq = 1/C1 + 1/C2 Capacitors in Circuits Remember series and parallel rules extend to any number of capacitors Keep simplifying until you find the equivalent capacitance for the whole circuit Resistors and Capacitors If you add a resistor to a charged capacitor, the capacitor will discharge through it If we charge a capacitor with a resistor in the circuit, it will also take time for the capacitor to fully charge t = RC This is the time to charge a capacitor to about 63% of the final value Charging a Capacitor Charge on the Capacitor We can write an expression for the charge on a capacitor: Q(t) = Ce[1-e(-t/t)] Capacitor charges rapidly at first and then the rate of charge separation slows At about t = 4t the capacitor is nearly fully charged Time Curve Meters We use meters to measure current, resistance, capacitance, voltage, etc. Want to minimize their effect Using an Ammeter Using a Voltmeter Types of Meters Ammeter Must be placed in series Voltmeter Must be placed in parallel Next Time Read 22.1-22.2 Homework Ch 21, P: 29, Ch 22, P: 2 Final: Section 1: Tuesday, Feb 25, 9-11 am Section 2: Thursday, Feb 27, Noon-2pm