Short Version : 25. Electric Circuits

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Short Version 25. Electric Circuits
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Electric Circuit collection of electrical
components connected by conductors.
Examples Man-made circuits flashlight, ,
computers. Circuits in nature nervous systems,
, atmospheric circuit (lightning).
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25.1. Circuits, Symbols, Electromotive Force
Common circuit symbols
All wires perfect conductors ? V const on
wire
Electromotive force (emf) device that maintains
fixed ?V across its terminals.
E.g., batteries (chemical), generators
(mechanical), photovoltaic cells (light), cell
membranes (ions).
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m q
Collisions resistance
g E
Lifting emf
Ideal emf no internal energy loss.
Energy gained by charge transversing battery q
E ( To be dissipated as heat in external R. )
Ohms law
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25.2. Series Parallel Resistors
Series resistors I same in every component
Same q must go every element.
?
For n resistors in series
Voltage divider
n 2
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Real Batteries
Model of real battery ideal emf E in series
with internal resistance Rint .
I means V drop I Rint
? Vterminal lt E
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Example 25.2. Starting a Car
Your car has a 12-V battery with internal
resistance 0.020 ?. When the starter motor is
cranking, it draws 125 A. Whats the voltage
across the battery terminals while starting?
Battery terminals
Voltage across battery terminals
Typical value for a good battery is 9 11 V.
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Parallel Resistors
Parallel resistors V same in every component
?
For n resistors in parallel
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Analyzing Circuits

• Tactics
• Replace each series parallel part by their
  single component equivalence.
• Repeat.

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Example 25.3. Series Parallel Components
Find the current through the 2-? resistor in the
circuit.
Equivalent of parallel 2.0-? 4.0-? resistors
?
Equivalent of series 1.0-?, 1.33- ? 3.0-?
resistors
Total current is
Voltage across of parallel 2.0-? 4.0-?
resistors
Current through the 2-? resistor
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25.3. Kirchhoffs Laws Multiloop Circuits

• Kirchhoffs loop law
• V 0 around any closed loop.
• ( energy is conserved )

• Kirchhoffs node law
• I 0 at any node.
• ( charge is conserved )

This circuit cant be analyzed using series and
parallel combinations.
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Multiloop Circuits
Problem Solving Strategy
INTERPRET Identify circuit loops and nodes.
Label the currents at each node, assigning a
direction to each.

• DEVELOP
• Apply Kirchhoff s node law to all but one
  nodes. ( Iin gt 0, Iout lt 0 )
• Apply Kirchhoff s loop law all independent
  loops
• Batteries ?V gt 0 going from ? to terminal
  inside the battery.
• Resistors ?V ? I R going along I.
• Some of the equations may be redundant.

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Example 25.4. Multiloop Circuit
Find the current in R3 in the figure below.
Node A
Loop 1
Loop 2
?
?
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Application Cell Membrane
Hodgkin-Huxley (1952) circuit model of cell
membrane (Nobel prize, 1963)
Resistance of cell membranes
Membrane potential
Time dependent effects
Electrochemical effects
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25.4. Electrical Measurements
A voltmeter measures potential difference
between its two terminals.
Ideal voltmeter no current drawn from circuit ?
Rm ?
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Example 25.5. Two Voltmeters
You want to measure the voltage across the 40-?
resistor. What readings would an ideal
voltmeter give? What readings would a voltmeter
with a resistance of 1000 ? give?
(a)
(b)
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Ammeters
An ammeter measures the current flowing through
itself.
Ideal voltmeter no voltage drop across it ?
Rm 0
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Ohmmeters Multimeters
An ohmmeter measures the resistance of a
component. ( Done by an ammeter in series with a
known voltage. )
Multimeter combined volt-, am-, ohm- meter.
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25.5. Capacitors in Circuits
Voltage across a capacitor cannot change
instantaneously.
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The RC Circuit Charging
C initially uncharged ? VC 0
Switch closes at t 0. VR (t 0) E ? I
(t 0) E / R C charging VC ? ? VR ? ?
I ? Charging stops when I 0.
VR ? but rate ?
I ? but rate ?
VC ? but rate ?
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?
?
VC 2/3 E
I 1/3 E/R
Time constant RC
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The RC Circuit Discharging
C initially charged to VC V0
Switch closes at t 0. VR VC V ? I 0
V0 / R C discharging VC ? ? VR ? ? I
? Disharging stops when I V 0.
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Example 25.6. Camera Flash
A camera flash gets its energy from a 150-?F
capacitor requires 170 V to fire. If the
capacitor is charged by a 200-V source through an
18-k? resistor, how long must the photographer
wait between flashes? Assume the capacitor is
fully charged at each flash.
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RC Circuits Long- Short- Term Behavior
For ?t ltlt RC VC ? const, ? C replaced by
short circuit if uncharged. ? C replaced by
battery if charged.
For ?t gtgt RC IC ? 0, ? C replaced by open
circuit.
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Example 25.7. Long Short Times

• The capacitor in figure is initially uncharged.
• Find the current through R1
• the instant the switch is closed and
• a long time after the switch is closed.

(a)
(b)