Download Electrical Energy And Power, And Emf

Electrical Energy And Power, And Emf
Dr Miguel Cavero
August 7, 2014
Energy And Power, And Emf
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Energy
Consider a component in a circuit with a potential difference ∆V
across it and a current I through it.
There is work done (q∆V ) on the charge by the electric field. The
potential energy of a positive charge decreases as it moves through
the component (the charge ”falls” from a point of higher potential to a
point of lower potential).
Does the charge gain kinetic energy?
Energy And Power, And Emf
Electrical Energy And Power
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Energy
Consider a component in a circuit with a potential difference ∆V
across it and a current I through it.
The current - which is the rate of flow of charge ∆q/∆t - entering the
component must be the same as the current leaving it.
The energy q∆V is transferred to the circuit component.
Energy And Power, And Emf
Electrical Energy And Power
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Energy
What happens if the potential difference across the component is
negative?
In this case, there is a net transfer of energy out of the component.
The component acts as a source, delivering electrical energy to a
circuit.
Energy And Power, And Emf
Electrical Energy And Power
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Energy
When electrical energy is transferred to a component, that component
is referred to as a load.
The load in a circuit converts electrical energy into other forms.
A load might be a resistor, that converts electrical energy into thermal
energy (like the coils in a toaster), or a motor, that converts electrical
energy into mechanical energy (to do work).
When electrical energy is transferred out of a component, that
component is referred to as a source.
A battery is an example of a source. It converts chemical energy into
electrical energy, which is available to the circuit the source is
connected to.
Energy And Power, And Emf
Electrical Energy And Power
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Rate Of Change Of Energy
Recall from mechanics, that power P is defined as the (time) rate of
work done:
W
P =
∆t
The work done W on charges moving through a component is q∆V is
equal to the energy transferred into/out of the component.
The power (the rate of energy transferred into/out of the component) is
P
q∆V
∆t
= ∆V I
=
The SI unit of power is the watt, W (1 W = 1 V A = 1 J C−1 × 1 C s−1 ).
Energy And Power, And Emf
Electrical Energy And Power
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Power In A Resistor
In the case where the load is a resistor, the potential difference across
the resistor R is given by Ohm’s Law
∆V = IR
where I is the current through the resistor.
The electrical power delivered to the resistor is
P
= ∆V I
= (IR)I = I 2 R
∆V
(∆V )2
= ∆V
=
R
R
Energy And Power, And Emf
Power Into A Pure Resistor
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The Kilowatt-Hour
Electricity is generally measured and charged for in terms of electrical
energy.
The kilowatt-hour (kWh) is defined as the total work done in one hour
when the power is 1 kW = 1000 W.
1 kWh = 1000 W × 3600 s = 3.6 × 106 J = 3.6 MJ
Note: the kilowatt-hour is a unit of energy (or work) and not power.
Energy And Power, And Emf
Commercial Unit Of Electrical Energy
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Steady Current
For an electrical component (such as a resistor) to have a steady
current, it must be part of a complete circuit, sometimes referred to a
closed loop.
There can be no steady motion of charge in an isolated electrical
component.
To maintain a steady current in a (complete) circuit, charge carriers
need electric potential energy to complete one loop of the circuit.
Consider a fountain in a garden. At the point where the water comes
out, it has gravitational potential energy compared to the ground, so
the water falls before collecting in a pool at the bottom.
A pump then increases the potential energy of the water to repeat the
process.
Energy And Power, And Emf
Emf
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Electric Potential Energy
Consider a simple circuit of three resistors in series.
The electric potential drops across each of the resistors. The potential
energy for any (positive) charge decreases as it moves through the
circuit.
Energy And Power, And Emf
Emf
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Electric Potential Energy
For the charge to move around the circuit again, it must gain potential
energy from somewhere.
Energy And Power, And Emf
Emf
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Emf
A device that increases the potential energy of a charge in a circuit is
referred to a source of emf. An example is a battery.
The emf, denoted by E, is like a charge ”pump” - moving a positive from
a point of low electric potential to a point of higher electric potential.
Note that an emf is not a force.
An emf is a work per unit charge, so it is dimensionally the same as an
electric potential.
The SI unit of an emf is the volt, V.
A battery that has an emf of 1.5 V does 1.5 J of work on every qaunity
of charge of 1 C that passes through it.
Energy And Power, And Emf
Emf
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Emf
The circuit could look like this:
Conventional current direction means that the current moves in a
clockwise manner in this circuit, from the positive terminal (the
high-potential side) to the negative terminal (low-potential side).
Energy And Power, And Emf
Emf
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An Example
In the circuit above, the battery has an emf of E = 12 V and the value
of the three resistors are as follows: R1 = 2 Ω, R2 = 1 Ω and R3 = 3 Ω.
What is the current flowing in the circuit?
The current I is:
12
E
I=
=
= 2A
Req
6
Energy And Power, And Emf
Emf
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An Example
In the circuit above, the battery has an emf of E = 12 V and the value
of the three resistors are as follows: R1 = 2 Ω, R2 = 1 Ω and R3 = 3 Ω.
What is the potential difference across R3 , the 3 Ω resistor?
The potential difference ∆V3 across R3 is:
∆V3 = IR3 = 2 × 3 = 6 V
Energy And Power, And Emf
Emf
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An Example
In the circuit above, the battery has an emf of E = 12 V and the value
of the three resistors are as follows: R1 = 2 Ω, R2 = 1 Ω and R3 = 3 Ω.
What is the power delivered to R3 ?
P = ∆V3 I = I 2 R3 =
Energy And Power, And Emf
(∆V3 )2
= 6 × 2 = 12 W
R3
Emf
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