Chapter 18 Electric Currents

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Chapter 18Electric Currents
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Simple Electric Cell

• Two dissimilar metals or carbon rods in acid
• Zn ions enter acid leaving terminal negative
• Electrons leave carbon making it positive
• Terminals connected to external circuit
• Battery referred to several cells originally

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Electric Current

• If we connect a wire between the two terminals
  electrons will flow out of the negative terminal
  and toward the positive terminal? we have an
  electric current.
• Electric current I is defined as the net amount
  of charge that flows past a given point per unit
  time.

• 1 C/s 1A (ampere)
• An ampere is a large current and often currents
  are mA (10-3 A) or ?A (10-6 A).

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Electric Circuit

• It is necessary to have a complete circuit in
  order for current to flow.
• The symbol for a battery in a circuit diagram is

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Conventional current direction is opposite to
actual electron flow direction which is to .
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Ohms Law

• For wires and other circuit devices, the current
  is proportional to the voltage applied to its
  ends
• I ?
  V
• The current also depends on the amount of
  resistance that the wire offers to the electrons
  for a given voltage V. We define a quantity
  called resistance R such that
• V I R (Ohms Law)
• The unit of resistance is the ohm which is
  represented by the Greek capital omega (?).
• Thus

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Resistors

• A resistor is a circuit device that has a fixed
  resistance.

Resistor
Circuit symbol
Resistors obey Ohms law but not all circuit
devices do (semi-conductor diode, LED)
Resistor
non-ohmic device
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Example A person experiences a mild shock if a
current of 80 ?A flows along a path between the
thumb and the index finger. The resistance of
this path is 4.0x105 ? when the skin is dry and
2000 ? when the skin is wet. Calculate the
minimum voltage difference between these two
points that will produce a mild shock.
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Example A person experiences a mild shock if a
current of 80 ?A flows along a path between the
thumb and the index finger. The resistance of
this path is 4.0x105 ? when the skin is dry and
2000 ? when the skin is wet. Calculate the
minimum voltage difference between these two
points that will produce a mild shock.
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Example Calculate the number of electrons per
second that flow past a point on the skin in the
previous example.
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Example Calculate the number of electrons per
second that flow past a point on the skin in the
previous example.
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Power in Electric Circuits

• Electrical circuits can transmit and consume
  energy.
• When a charge Q moves through a potential
  difference V, the energy transferred is QV.
• Power is energy/time and thus

and thus
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Notes on Power

• The formula for power applies to devices that
  provide power such as a battery as well as to
  devices that consume or dissipate power such as
  resistors, light bulbs and electric motors.

• For ohmic devices, the formula for power can be
  combined with Ohms Law to give other versions

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Household Power

• Electric companies usually bill by the
  kilowatt-hour (kWh.) which is the energy consumed
  by using 1.0 kW for one hour.
• Thus a 100 W light bulb could burn for 10 hours
  and consume 1.0 kWh.
• Electric circuits in a building are protected by
  a fuse or circuit breaker which shuts down the
  electricity in the circuit if the current exceeds
  a certain value. This prevents the wires from
  heating up when carrying too much current.

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Connection of Household Appliances
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• Example A person turns on a 1500 W electric
  heater, a 100 W hair dryer and then a 300 W
  stereo. All of these devices are connected to a
  single 120 V household circuit that is connected
  to a 20 A circuit breaker. At what point will the
  circuit breaker trip off?

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• Example A person turns on a 1500 W electric
  heater, a 100 W hair dryer and then a 300 W
  stereo. All of these devices are connected to a
  single 120 V household circuit that is connected
  to a 20 A circuit breaker. At what point will the
  circuit breaker trip off?

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• Example If electricity costs 0.1379 per kWh in
  Nova Scotia, calculate the cost of operating all
  the appliances in the previous problem for 2.0
  hours.

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• Example If electricity costs 0.1379 per kWh in
  Nova Scotia, calculate the cost of operating all
  the appliances in the previous problem for 2.0
  hours.

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Microscopic View of Current

• Read Example 18-13 on page 545. It studies a
  5.0A current in a copper wire that is 3.2 mm in
  diameter. It finds that the average free
  electron moves with a velocity of 4.7 x 10-5 m/s
  in the direction of the current. This is called
  the drift velocity.
• It also assumes the free electrons behave like
  an ideal gas and calculates that the thermal
  velocity of the average electron is 1.2 x 105
  m/s.
• Thus in a wire carrying a current, the electron
  motion is largely random with a slight tendency
  to move in the direction of the current. Thus if
  you could see electrons in a wire carrying
  current they would appear to be moving randomly.

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Summary of Units
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Chapter 19

• DC Circuits

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EMF

• Devices that supply energy to an electric circuit
  are referred to as a source of electromotive
  force. Since this name is misleading, we just
  refer to them as source of emf (symbolized by ?
  and a slightly different symbol in the book.)
• Sources of emf such as batteries often have
  resistance which is referred to as internal
  resistance.

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Terminal Voltage

• We can treat a battery as a source of ? in series
  with an internal resistor r.
• When there is no current then the terminal
  voltage is Vab ?
• But with current I we have

• The internal resistance is small but increases
  with age.

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Circuit Symbols
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Resistors in Series - Derivation

• We want to find the single resistance Req that
  has the same effect as the three resistors R1,
  R2, and R3.
• Note that the current I is the same throughout
  the circuit since charge cant accumulate
  anywhere.
• V is the voltage across the battery and also
• V V1 V2 V3
• Since V1 I R1 etc., we can say

The equivalent equation is VIReq and thus
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Summary - Resistors in Series
The current I is the same throughout the circuit
since charge cant accumulate anywhere.
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Resistors in Parallel - Derivation

• This is called a parallel circuit
• Notice V1 V2 V3 V
• Since charge cant disappear, we can say

• We can combine these equations with
• V IReq to give

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Summary - Resistors in Parallel

• The electric potential (voltage) is the same
  across each resistor
• V1 V2 V3
• The current through the battery splits several
  ways
• I I1 I2 I3
• Can be 2, 3 or more resistors in parallel.

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Example A 3.0 V battery is connected to three
resistors as shown. Calculate the resistance of
the equivalent circuit and the power dissipated
in the equivalent circuit. R1 500 O, R2 1000
O and R3 2000 O.
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Example A 3.0 V battery is connected to three
resistors as shown. Calculate the resistance of
the equivalent circuit and the power dissipated
in the equivalent circuit. R1 500 O, R2 1000
O and R3 2000 O.
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Example From the previous example, calculate the
current and the power dissipated in each resistor
and the total power dissipated in the circuit.
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Example From the previous example, calculate the
current and the power dissipated in each resistor
and the total power dissipated in the circuit.
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Example A 3.0 V battery is connected to 4
resistors as shown. Calculate the resistance of
the equivalent circuit and the current in the
equivalent circuit. R1 500 O, R2 1000 O, R3
1000 O, and R4 2000 O.
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Example A 3.0 V battery is connected to 4
resistors as shown. Calculate the resistance of
the equivalent circuit and the current in the
equivalent circuit. R1 500 O, R2 1000 O, R3
1000 O, and R4 2000 O.
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Ammeter

• To measure current ammeter must be connected in
  series.
• Must have small internal resistance or it will
  reduce current and give a faulty measurement.

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Voltmeters

• To measure voltage difference, it must be
  connected in parallel.
• Must have high internal resistance or it will
  draw too much current which reduces voltage
  difference and gives a faulty measurement.