Transcript Electric Current and Circuits

Electric Current and
Circuits
What is Current?
Electric current is a flow of electric charge
I = Q/t
 By convention from + to –
 Actually electrons flow away from – and
toward +
 Symbol of current is I
 Unit is the ampere (A)
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1 Ampere = 1
Coulomb/Second
Batteries
Batteries produce charge continuously from
chemical reactions
 Consist of two dissimilar metals in an
electrolyte (liquid, paste, or gel)
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Current is Flow of Charge in a
Conductor
 I = DQ/Dt
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Example: A steady current of 4.0 amperes
flows in a wire for 3 minutes. How much
charge passes through the wire?
720 Coulombs
Charge = Current x time
Q
= I Dt
 How
many coulombs of charge
will a 60 amp-hour battery deliver?
216,000 Coulombs
Current Flows in an Electric
Circuit
A continuous conducting path is called a
circuit
 Current flows through the
wires from one terminal
of the battery to another
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Courtesy http://www.uce.ac.uk/education/research/cript/electricity%20book/water%20model%20electric%20circuit.htm
Current Must Flow in a
Continuous Loop
If there is a break anywhere in the loop
circuit is OPEN. No current flows.
 If no break circuit is CLOSED. Current
flows.
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Current Must Flow in a
Continuous Loop
If there is a break anywhere in the loop
circuit is OPEN. No current flows.
 If no break circuit is CLOSED. Current
flows.
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What Really Happens
Potential difference between terminals of
battery sets up an electric field in the wire
and just outside parallel to it
 Free electrons leave negative terminal of
battery, pass through circuit and re-enter
battery at positive terminal

Sponge analogy
Wire is full of electrons
 When you put one in, another comes out the
other end
 Like saturated sponge
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Ohm’s Law
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Current flow is proportional to voltage
Inversely proportional to resistance
Resistance is constant of proportionality
I is current
V
=IR
 I = V/R
R=V/I
Ohm’s Law
Ohm’s Law V = IR
What happens to current if you increase V?
 What happens if you increase R?

UNITS
 Voltage
Volt (V)
 Current
Amperes (A)
 Resistance Ohm()
Draw a Graph of V as a function
of I for a Resistor of Constant R
V = IR
Resistance
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Resistance of a metal wire:
R = rL/A r is resistivity
L is length of wire
A is cross sectional area
Silver has lowest resistivity
Copper is almost as low
Gold and Aluminum low too
Superconductivity
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Resistance of certain materials
becomes zero at low temperatures
Niobium-titanium wire at 23K
Yttrium-Barium-Copper-Oxygen at 90K
Bismuth-strontium-calcium copper oxide
Can make strong electromagnets that do not
require power
Japanese Maglev Train goes 329 mph
Power

Power = Current x Voltage
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Power = energy/time = QV/time = IV
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Unit: watt
Examples (P = IV; V = IR)
What power does a 6 amp toaster operating
at 120 volts use? 720 watts
 What power is used by a 120 volt motor
with an operating resistance of 10 ohms?
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1440 w
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What current is drawn by a 100 watt
headlamp on a car (12 volt)? What is its
operating resistance?
8.33 A; 1.44 ohms()
Cost of an Electric Heater
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How much would it cost to operate a 1500
watt electric heater continuously for one
month if the power company charges $.13
per kwh? $140.40
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(b) What is the resistance of this heater
(assume V = 120V) 9.6 ohms
Power
IV
= I2R = V2/R
Will it Blow?
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A 1200 watt hair dryer, a 6 amp pump
motor, and a 250 watt TV are operating on
the same 20 amp circuit. How many 100
watt light bulbs could be turned on without
overloading the circuit (and blowing the
fuse or tripping the breaker?)
AC - DC
DC is direct current.
 Steady
 Comes from battery or power supply
 AC is alternating current
 Sine wave with frequency of 60 Hz (in
U.S.)
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AC
Electric Power
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Power = energy transformed/time = QV/t
P = IV unit: watt
Since V = IR
P = IV = I2R = V2/R
In power transmission, why is high voltage
advantageous?
Series Resistive Circuit
Full current goes through all circuit
components
I
Batteries in Series
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When batteries or other sources of potential are
connected in series, the total potential difference is
the algebraic sum of the separate potentials.
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6V + 6V = 12V
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Another example: a 9 volt radio battery consists
of 6 1.5 volt cells in series.
Batteries in Parallel
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The voltages do not add but more current is
available
Parallel Resistive Circuit
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Same voltage across all circuit elements
IT = I1 + I2 + I3 +
V/RT = V/R1 + V/R2 + V/R3
1/RT = 1/R1 + 1/R2 + 1/R3 +
Only Two Resistors
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RT = R1R2/(R1 + R2)
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Adding a parallel resistor reduces total
resistance
Summary
In a series circuit there is only one current,
but many voltages (across each resistance
and the battery)
 In a parallel circuit there is only one voltage
but many currents (in each of the branches)
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Solving Circuits
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Can have both series and parallel parts
Find equivalent resistances starting from point
furthest away from battery
Use Kirchoff’s Rules
 Voltages around a closed loop add to
zero(conservation of energy)
 Sum of currents entering a junction equals sum
of currents leaving(conservation of charge)
Find all Possible Currents and
Voltages
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Around loop voltage “drops” add up to battery
voltage – use to find certain voltages by
subtraction
Keep applying Ohm’s Law
At junction, currents divide up in inverse
proportion to resistance they “see”
If you have two loops with batteries or wires that
cross you may need to apply Kirchoff’s Laws
formally to obtain simultaneous equations
EMF and Terminal Voltage
Battery is said to be a “seat” of
electromotive force or emf
 Emf is not a force
 Real batteries have internal resistance r
 Terminal voltage is less than emf when
internal resistance is accounted for
 Vab = E - Ir
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Capacitors in Parallel
Total charge is sum of charges on individual
capacitors
 Q = Q1 +Q2 + Q3 = C1V +C2V + C3V
 Q = CT V
 CTV = C1V +C2V + C3V
 CT = C1 + C2 + C3
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Capacitors in Series
Charge same on each capacitor
 Q = CT V
 V = V1 + V2 + V3
 Q/CT = Q/C1 + Q/C2 + Q/C3
 1/CT = 1/C1 + 1/C2 +1/C3
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Ammeters and Voltmeters
Ammeters have low resistance and are
placed in series
 Voltmeters have high resistance and are
placed in parallel
 Multimeter measures current, voltage and
resistance
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