Transcript Review PPT - Hss-1.us

Electric Circuits
Just like we can use pipes to carry water, we can use
wires to carry electricity. We can use this concept to
understand electric circuits.
The flow of water through pipes is caused by pressure
differences, and the flow is measured by volume of
water per time.
The flow of electricity is cause by a voltage or electro
potential difference and the flow or current is measure
by the flow of charge per time amperage.
Voltage
In electricity, the concept of voltage will be
like pressure. Water flows from high
pressure to low pressure (this is consistent with
the analogy that Voltage is like height since DP =
rgh for fluids) ; electricity flows from high
voltage to low voltage.
PEel = k q1 q2 / r12
Vat 2 due to 1 = PEof 2 / q2
volt = Joule / Coulomb
Voltage Sources:
batteries and power supplies
A battery or power supply supplies voltage.
This is analogous to what a pump does in a
water system.
Current
Charges flows in electricity.
How do we measure this flow? By Current:
current = I = Dq / Dt
UNITS: Amp(ere) = Coulomb / second
Circuit Elements
In this first part of the course we will consider
two of the common circuit elements:
capacitor
resistor
The capacitor is an element that stores
charge for use later (like a water tower).
- Example UPS, TVs
The resistor is an element that “resists” the
flow of electricity.
- There are resistors, Light bulbs, stovers
and so on.
Capacitance
We define capacitance as the amount of
charge stored per volt: C = Qstored / DV.
UNITS: Farad = Coulomb / Volt
Just as the capacity of a water tower depends
on the size and shape, so the capacitance of
a capacitor depends on its size and shape.
Just as a big water tower can contain more
water per foot (or per unit pressure), so a
big capacitor can store more charge per volt.
Two basic ways
There are two basic ways of connecting two
capacitors: series and parallel.
In series, we connect capacitors together like
railroad cars; using parallel plate capacitors
it would look like this:
+
-
+
-
high V
low V
C1
C2
1/CEffective Series = 1/C1 + 1/C2 =
Series
If we include a battery as the voltage source,
the series circuit would look like this:
C1
+
Vbat
C2
Note that there is only one way around the
circuit, and you have to jump BOTH
capacitors in making the circuit - no choice!
Parallel
In a parallel hook-up, there is a branch point
that allows you to complete the circuit by
jumping over either one capacitor or the
other: you have a choice!
High V
C1
C2
Low V
Parallel Circuit
If we include a battery, the parallel circuit would
look like this:
+
Vbat
+
C1
Ceff = C1 + C2 .
+
C2
Review of Formulas
For capacitors in SERIES we have:
1/Ceff = 1/C1 + 1/C2 .
For capacitors in PARALLEL we have:
Ceff = C1 + C2 .
Note that adding in series gives Ceff being
smaller than the smallest, while adding in
parallel gives Ceff being larger than the
largest!
Resistance
Electrical Resistance - anything in a circuit that
slows the flow of electrons down
Current is somewhat like fluid flow. Recall that it
took a pressure difference to make the fluid flow
due to the viscosity of the fluid and the size (area
and length) of the pipe. So to in electricity, it
takes a voltage difference to make electric current
flow due to the resistance in the circuit.
Resistance
By experiment we find that if we increase the
voltage, we increase the current: V is
proportional to I. The constant of
proportionality we call the resistance, R:
V = I*R
Ohm’s Law
UNITS: R = V/I so Ohm = Volt / Amp.
Electrical Power
The electrical potential energy of a charge is:
PE = q*V .
Power is the change in energy with respect to time:
Power = DPE / Dt .
Putting these two concepts together we have:
Power = D(qV) / Dt = V(Dq) / Dt = I*V.
P = I2*R = V2/R = I*V
Connecting Resistors
There are two basic ways of connecting two
resistors: series and parallel.
In series, we connect resistors together like
railroad cars; this is just like we have for
capacitors:
+
-
+
high V
-
low V
R1
R2
Formula for Series:
To see how resistors combine to give an
effective resistance when in series, we can
look either at
R1
I
V = I*R,
or at
+
V1 V
R2
Vbat
2
R = rL/A .
Reff = R1 + R2.
Formula for Parallel Resistors
The result for the effective resistance for a
parallel connection is 1/Reff = 1/R1 + 1/R2 .
.
Itotal
+
Vbat
I1
-
R1 I2
R2
Review:
Capacitors: C = Q/V
PE = ½CV2; C// = KA/[4pkd]
Series: 1/Ceff = 1/C1 + 1/C2
Parallel: Ceff = C1 + C2
series gives smallest Ceff, parallel gives largest
Resistors: V = IR
Power = IV; R = rL/A
Series: Reff = R1 + R2
Parallel: 1/Reff = 1/R1 + 1/R2
series gives largest Reff, parallel gives smallest