Electric Current and Circuits

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Electric Current and Circuits
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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
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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
• Example A steady current of 4.0 amperes flows
  in a wire for 3 minutes. How much charge passes
  through the wire?

720 Coulombs
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Charge Current x time

• Q I Dt
• How many coulombs of charge will a 60 amp-hour
  battery deliver?

216,000 Coulombs
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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

Courtesy http//www.uce.ac.uk/education/research/c
ript/electricity20book/water20model20electric2
0circuit.htm
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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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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

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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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Ohms Law

• Current flow is proportional to voltage
• Inversely proportional to resistance
• Resistance is constant of proportionality
• I is current
• V I R
• I V/R RV/I

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Ohms Law

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Ohms Law V IR

• What happens to current if you increase V?
• What happens if you increase R?

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UNITS

• Voltage Volt (V)
• Current Amperes (A)
• Resistance Ohm(?)

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Draw a Graph of V as a function of I for a
Resistor of Constant R
V IR
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Resistance

• 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

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Superconductivity

• 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

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Power

• Power Current x Voltage
• Power energy/time QV/time IV
• Unit watt

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Examples (P IV V IR)

• What power does a 6 amp toaster operating at 120
  volts use?
• What power is used by a 120 volt motor with an
  operating resistance of 10 ohms?
• What current is drawn by a 100 watt headlamp on a
  car (12 volt)? What is its operating resistance?

720 watts
1440 w
8.33 A 1.44 ohms(W)
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Cost of an Electric Heater

• How much would it cost to operate a 1500 watt
  electric heater continuously for one month if the
  power company charges .13 per kwh?
• (b) What is the resistance of this heater
• (assume V 120V)

140.40
9.6 ohms
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Power

• IV I2R V2/R

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Will it Blow?

• 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?)

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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
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Electric Power

• 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?

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Series Resistive Circuit

• Full current goes through all circuit components

I
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Batteries in Series

• When batteries or other sources of potential are
  connected in series, the total potential
  difference is the algebraic sum of the separate
  potentials.
• 6V 6V 12V
• Another example a 9 volt radio battery consists
  of 6 1.5 volt cells in series.

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Batteries in Parallel

• The voltages do not add but more current is
  available

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Parallel Resistive Circuit

• 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

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Only Two Resistors

• RT R1R2/(R1 R2)
• Adding a parallel resistor reduces total
  resistance

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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

• Can have both series and parallel parts
• Find equivalent resistances starting from point
  furthest away from battery
• Use Kirchoffs 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)

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Find all Possible Currents and Voltages

• Around loop voltage drops add up to battery
  voltage use to find certain voltages by
  subtraction
• Keep applying Ohms 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 Kirchoffs Laws
  formally to obtain simultaneous equations

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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 CTV
• CTV C1V C2V C3V
• CT C1 C2 C3

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Capacitors in Series

• Charge same on each capacitor
• Q CTV
• 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