Final Exam Current and the Motion of Charges-the rate of flow of electrical charge through a cross-sectional area I = ΔQ/Δt (1A = 1 C/s) I = qnAv d , n = # of free charges = (ρN avog. )/M molar , v d = drift velocity Resistance and Ohm’s Law potential drop V = V a – V b = EΔL Resistance : ratio of potential drop to the current R = V/I (1Ω = 1V/A) R = ρL/A-resistance of a conductivity wire Energy in Electrical Circuits P = IV = I 2 R = V 2 /R (1 watt = 1 J/s)-power dissipated (potential energy loss per unit time) in the conducting segment-electromotive force (emf) supplies energy to a circuit (volts), has the same equations as V-charge through a source of emf (battery), PE increased by ΔQЄ P = IЄ-rate at which energy is supplied by the source V a,+ – V b,-= Є – Ir, r = internal resistance of battery I = Є/(R + r) W = QЄ, Q = total charge the battery can deliver-total energy stored in a battery Combinations of Resistors Series: R eq = R 1 + R 2 + R 3 +… V = IR 1 + IR 2 = I(R 1 + R 2 ) Parallel: R eq = (1/R 1 + 1/R 2 + 1/R 3 +…)-1 V = I 1 R 1 = I 2 R 2-the current divides into each branch proportionally Kirchhoff’s Rules 1. when any closed loop surface is traversed, the sum of the changes in potential must = 0 2. at any junction (branch point), the sum of the currents into the junction must equal the sum of the currents out of the junction Single Loop Circuits: ex.) –IR 1 – Є 2 – Ir 2 – IR 2 + Є 1 – Ir 1 = 0 Multi-Loop Circuits:-the ΔV must still sum to 0 for each loop, do the inner loop then th outer loop RC Circuits-contain a resistor and a capacitor Discharging a capacitor: no battery, switch is closed and a current flows, current = the rate of decrease of
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