L07

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5 Οκτ 2013 (πριν από 3 χρόνια και 10 μήνες)

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Chapter 27 DC Circuits

DC Circuits

Combining Resistors and
Capacitors

Time Dependent Circuits

Work done by a battery on charge


Here

Real Battery and Single Loop circuits… What’s the current ?

Conservation of energy:

Kirchoff’s first Law: Sum of voltages in a closed loop is zero.

Real Circuit with ammeter
and voltmeter

Equivalent Resistance

Resistors in Series

Series requirements


Conservation of energy


Potential differences add


Current is constant

Apply Ohm’s Law to each resistor

Resistors in parallel

Parallel requirements


Charge conservation


Currents must add


Potential difference is
same across each resistor

Apply Ohm’s Law to each resistor

Example 27
-
2

What is current through
battery?

What is current
through i
2


and


i
3
?

Kirchhoff’s Rules

1
The algebraic sum of the currents
entering a junction is zero.
(
Conservation

of Charge
)

2
The algebraic sum of the changes in
electric potential difference around
any closed circuit loop is zero.
(
Conservation of Energy
)

Signs for Rule 2

The direction of travel when traversing
the loop is from a to b.

Problem 27
-
3

Find the currents in each of the
three legs of the circuit,

Three unknowns, need three equations.

Also, since batteries are in the loops, cannot reduce the resistances
since none in parallel or series

Example or Applying Kirchhoff’s
Rules

Apply Kirchhoff’s first rule to
the three wire junction at
the bottom of the diagram

Apply Kirchhoff’s second
rule to the closed path in red,
traversing it clockwise

Apply Kirchhoff’s second rule
to the closed path in green,
traversing it clockwise

Note the sign changes for
some of the elements

Another, example: applying Kirchhoff’s Rules


Solve the equations
simultaneously for the values
if I. If I is negative the
current is in the opposite
direction

RC Circuits and Time dependence

Time dependence

Recall Lab 7! Resistor
slows down the charging

of the capacitor

Time dependent behavior
(transient) 2 cases: switch at

“a” or at “b”


a)
Charging

b)
discharging

a) Charging the Capacitor

Note:

is called the time constant

What are the units?

In position “a” Charging the
Capacitor

Use Kirchhoff’s Voltage
Loop rule

First order Differential Equation.
Solution, integrate once. Did this in
lab
-
6.

Can check that these are the
solutions by differentiation

What’s
V
R

across resistor?

Find the current and multiply by
R

Discharging Position b)

Kirchhoff's Voltage Law

Example: Time Constant


How long does it take the
capacitor to reach ½ its final
charge, if the capacitor is
uncharged at t = 0?

R=10


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