Announcements WebAssign HW Set 5 due this Friday Problems cover material from Chapters 18

1. Announcements • WebAssign HW Set 5 due this Friday • Problems cover material from Chapters 18 • My office hours today from 2 – 3 pm • or by appointment (I am away next week) • Exam 1 8:20 – 10:10 pm Wednesday, February 16 • Covers Ch. 15-18 • 20 questions • You should bring: • 8 ½ x 11 in formula sheet (handwritten only!) • Calculator (no cell phones) + spare batteries • pencils (spares) • UF ID • Room assignments: • QUESTIONS? PLEASE ASK!

2. From last time • emf • Internal resistance • Terminal voltage ΔV = ε – Ir • Resistors in Series • Same current Req = R1 + R2 + R3 + … • Resistors in parallel • Same voltage drop

3. Kirchhoff’s Rules I1 = I2 + I3 • Junction Rule • Sum of the currents entering a junction = the sum of the currents leaving the junction Σ Iin = Σ Iin • Conservation of charge • Loop Rule • Sum of the ΔV across all the elements around any closed circuit loop must be zero Σ Vloop = 0 • A statement of Conservation of Energy

4. More About the Loop Rule • Traveling around the loop from a to b • In (a), the resistor is traversed in the direction of the current, the potential across the resistor is –IR • In (b), the resistor is traversed in the direction opposite of the current, the potential across the resistor is +IR

5. Even More About the Loop Rule • In (c), the source of emf is traversed in the direction of the emf (from – to +), the change in the electric potential is +ε • In (d), the source of emf is traversed in the direction opposite of the emf (from + to -), the change in the electric potential is -ε

6. Problem-Solving Strategy – Kirchhoff’s Rules • Draw the circuit diagram and assign labels and symbols to all known and unknown quantities • Assign directions to the currents. • Apply the junction rule to any junction in the circuit • Apply the loop rule to as many loops as are needed to solve for the unknowns • Solve the equations simultaneously for the unknown quantities • Check your answers

7. Example Problem 18.26 • A dead battery is charged by connecting it to a live battery of another car with jumper cables. Determine the amount of current in the starter and in the dead battery.

8. RC Circuits • DC circuits containing capacitors and resistors, having time-varying currents/charges • When S is closed, the capacitor starts to charge • The capacitor charges until it reaches its maximum charge (Qmax = Cε) • Once the capacitor is fully charged, I 0

9. Charging Capacitor in an RC Circuit • The charge on the capacitor varies with time q(t) = Qmax(1 – e-t/RC) • Can define a time constant:  = RC •  is the time required for the q to increase from zero to 63.2% (= 1 – e) of its maximum

10. Notes on Time Constant • In a circuit with a large time constant, the capacitor charges very slowly • The capacitor charges very quickly if there is a small time constant • After t = 10 t, the capacitor is over 99.99% charged

11. Discharging Capacitor in an RC Circuit • When a charged capacitor is placed in the circuit, it can be discharged • q = Qe-t/RC • The charge decreases exponentially • At t =  = RC, the charge decreases to 0.368 Qmax • In other words, in one time constant, the capacitor loses 63.2% of its initial charge

12. Example Problem 18.33 • Consider a series RC circuit for which R = 1.0 MΩ, C = 5 μF, and ε = 30 V. Find the charge on the capacitor 10 s after the switch is closed.

13. Solution to 18.26

14. Solution to 18.33