Lecture 7 Circuits Chp. 28

1
Lecture 7 Circuits Chp. 28

• Cartoon -Kirchoffs Laws
• Opening Demo- transmission lines
• Physlet
• Topics
• Direct Current Circuits
• Kirchoffs Two Rules
• Analysis of Circuits Examples
• Ammeter and voltmeter
• RC circuits
• Demos
• Ohms Law
• Power loss in transmission lines
• Resistivity of a pencil
• Blowing a fuse
• Warm-up problems

2
Transmission line demo
3
Direct Current Circuits

1. The sum of the potential charges around a closed
   loop is zero. This follows from energy
   conservation and the fact that the electric field
   is a conservative force.

2. The sum of currents into any junction of a
closed circuit must equal the sum of currents out
of the junction. This follows from charge
conservation.
4
Example (Single Loop Circuit)

• No junction so we dont need that rule.
• How do we apply Kirchoffs rule?
• Must assume the direction of the current assume
  clockwise.
• Choose a starting point and apply Ohms Law as
  you go around the circuit.
• Potential across resistors is negative
• Sign of E for a battery depends on assumed
  current flow
• If you guessed wrong on the sign, your answer
  will be negative
• Start in the upper left hand corner.

5
Note that we could have simply added all
resistors and get the Req. and added the EMFs to
get the Eeq. And simply divided.
Put in numbers.
Suppose
amp
Sign of EMF Battery 1 current flows from - to
in battery E1 Battery 2 current flows from to
- in battery -E2 In 1 the electrical potential
energy increases In 2 the electrical potential
energy decreases
amp
Suppose
amp
We get a minus sign. It means our assumed
direction of current must be reversed.
6
Example with numbers
Quick solution
Question What is the current in the
circuit? Write down Kirchoffs loop
equation. Loop equation Assume current flow is
clockwise. Do the batteries first Then the
current.
7
Example with numbers (continued)
Question What are the terminal voltages of each
battery? 12V 2V 4V
8
Multiloop Circuits
Find i, i1, and i2
We now have 3 equations with 3 unknowns.
multiply by 2

• Kirchoffs Rules
• in any loop
• at any junction

multiply by 3
subtract them
Rule 1 Apply to 2 loops (2 inner
loops) a. b. Rule 2 a.
Find the Joule heating in each resistor Pi2R. Is
the 5V battery being charged?
9
Method of determinants for solving simultaneous
equations
For example solve for i
You try it for i1 and i2. See Appendix in your
book on how to use Cramers Rule.
10
Another example

• Find all the currents including directions.

Loop 1
Loop 2
multiply by 2 i i1 i2
11
Rules for solving multiloop circuits

1. Replace series resistors or batteries with their
   equivalent values.
2. Choose a direction for i in each loop and label
   diagram.
3. Write the junction rule equation for each
   junction.
4. Apply the loop rule n times for n interior loops.
5. Solve the equations for the unknowns. Use
   Cramers Rule if necessary.
6. Check your results by evaluating potential
   differences.

12
How does a capacitor behave in a circuit with a
resistor?
Charge capacitor with 9V battery with switch
open, then remove battery.
Now close the switch. What happens?
13
Discharging a capacitor through a resistor
What is the current I at time t?
14
Time constant RC
15
What is the current?
Ignore - sign
RC
16
How the charge on a capacitor varies with time as
it is being charged
17
(No Transcript)
18
Ohmmeter
19
Ammeter
20
Voltmeter
21
Warm up set 7

• Warm up set 7 Due 800 am Tuesday
• HRW6 28.TB.05. 119859 In the context of the
  loop and junctions rules for electrical circuits
  a
• junction is
• where a wire is connected to a battery
• where three or more wires are joined
• where a wire is bent
• where a wire is connected to a resistor
• where only two wires are joined
• 2. HRW6 28.TB.18. 119872 Two wires made of the
  same material have the same length but
• different diameter. They are connected in
  parallel to a battery. The quantity that is NOT
  the same
• for the wires is
• the electric field
• the electron drift velocity
• the current
• the current density
• the end-to-end potential difference