1. Resistors in Parallel R1 R2 i ε

2. Another example (with parallel R combos)
Sketch the diagram
Simplify using equivalent resistors
Label currents with directions
Use Junction Rule in labeling
Choose independent loops
Use Loop Rule
Solve simultaneous linear equations I1
Replace by equivalent R=2Ω first.
I3 = I1 + I2

3. Loop current example (with parallel R combos)
Sketch the diagram
Simplify using equivalent resistors
Label loop currents with directions
Use Loop currents I1 and I2
Choose interior clockwise loops
. Set up cononical equations in
. I1 I Ε format
I1 -I2
Replace by equivalent R=2Ω first.
I1 (12 +6) +I2 (-6) = +18 (Emf) Left loop
I1 (-6) + I2 (6+3+2) =+21 (Emf) Right loop
Note Symmetry of Equations

4. Finding Potential and Power in a Circuit
But what is I? Must solve for I first!
supplied by 12V battery
Just means 0 V here
dissipated by resistors
The rest?
into 4V battery (charging)

5. Ammeter and Voltmeter Ammeter: an instrument used to measure currents
It must be connected in series.
The internal resistance of an ammeter must be kept as small as possible.
Voltmeter: an instrument used to measure potential differences
It must be connected in parallel.
The internal resistance of a voltmeter must be made as large as possible.

6. Galvanometer Inside Ammeter and Voltmeter
Galvanometer: a device that detects small currents and indicates its magnitude. Its own resistance Rg is small for not disturbing what is being measured.
shunt resistor
galvanometer
Ammeter: an instrument used to measure currents
Voltmeter: an instrument used to measure potential differences
galvanometer

7. Reading quiz 1
Consider the charging of a capacitor C by battery with emf E through
an external resistor R. The final charge of the capacitor is QF. Which of the following statements is incorrect?
A| The energy delivered by the battery is E QF .
B| The energy stored in the capacitor 1/2 QF 2 /C.
C| The energy dissipated in the resistor is EQF /2.
D| The fraction of the energy delivered by the battery depends
the value of the resistor R.

8. Capacitor in RC Circuits
charging I
discharging ε
Switch closed at t=0. C initially charged, thus V0 = Q0/C across C and I0 = V0/R initially.
Switch closed at t=0. C initially uncharged, thus V0 = 0 across C and I0 = ε/R initially.
After a long time, C is fully charged and VC = ε across C and I0 = 0.
After a long time, C is fully discharged and VC = 0 across C and I∞ = 0.
time constant

9. Discharging a Capacitor in RC Circuits
Switch closed at t=0. Initially C is fully charged with Q0
Loop Rule: I
Convert to a differential equation
Solve it!

10. Q(t) during Discharging
time constant

11. Current I(t) during Discharging

12. Warm-up quiz 2
What’s the time constant in the following circuits. All resistors have the same resistance R, all capacitors have the same capacitance C.
3/5RC
2RC RC
4/9RC
6/4RC

13. Charging a Capacitor in RC Circuits
Switch closed at t=0
C initially uncharged, thus zero voltage across C.
Loop Rule:
3. Convert to a differential equation
Solve it!
(τ=RC is the time constant again)

14. Charge Q(t) during Charging
time constant

15. Current I(t) during Charging

16. Broken circuit = RC
110V
C very small. i.e. RC very small. Instantly discharged

17. Behavior of Capacitors
Charging
Initially, the capacitor behaves like a wire.
After a long time, the capacitor behaves like an open switch.
Discharging
Initially, the capacitor behaves like a battery.
After a long time, the capacitor behaves like an open switch

18. DOCCAM 2

20. Energy Conservation in Discharging a Capacitor
Energy lost by C
Power dissipated by R

21. Energy Conservation in Charging a Capacitor
Work done by battery
Energy stored in C
Power dissipated by R
The rest?
Independent of R
What if R=∞ ?
What if R=0 ?

22. PHYS :30 Quiz 3
All the capacitors below are identical and so are all the resistors. Which circuit have the shortest time constant? B A C E D

23. PHYS241 – 11:30 Quiz 3
All the capacitors below are identical and so are all the resistors. Which circuit have the longest time constant? C A B D E

24. PHYS241 - Quiz 12c
All the capacitors below are identical and so are all the resistors. Which circuit have the shortest time constant? C A B D E