•
•
•
•
•
•
•
•
Summer 2016 PH203, Aug 22, Day 6
Topic Outline
Chapter 23 Circuits
Sources of Current (emf)
Circuit Symbols
Kirchhoff’s Rules
Resistors in Series and Parallel
Analyzing Simple Circuits
Oh yeah, more complex ones also
(Capacitors too?)
Source of Current (emf)
Type
Current
induced via
Voltage
depends on
ac or dc?
Example(s)
Chemical
chemical reaction
chemical make-up and
number of cells
combined
dc
battery
Electromagnetic
movement of wire
through magnetic field
construction of device
and speed
either
generator
alternator
Thermoelectric
temperature gradient
between ends of
joined, dissimilar
metals
metals used and
temperature gradient
dc
thermocouple
Photoelectric
light (e.m. radiation)
absorbed by certain
semiconductors
material used and light
intensity
dc
solar cell
Piezoelectric
mechanical
deformation of certain
crystals
crystal type and
amount of deformation
ac
piezoelectric
microphone
All of these devices can have an “inverse” effect if current is supplied. Current
input to a generator can cause it to turn – a motor. An electric signal input to a
piezoelectric crystal can be a speaker (tweeter).
Some Common Circuit Symbols
battery
cell
ground
resistor
variable resistor
wire
capacitor
switch
light bulb
junction (of wires)
crossing wires (not joined)
ammeter
voltmeter
galvanometer
inductor
diode
ac generator
Circuit Elements and Potential
• Batteries (emf sources generally) increase the potential of
charges that make up current.
• Resistors, light bulbs, motors, anything that uses electric
energy, decrease the potential of charges in the circuit.
• Analyzing circuits requires keeping careful track of the
current in the various paths of the circuit and the gains and
losses in potential in the various elements within the circuit.
• Conservation of energy, charge and current means that all
potential changes and currents must be accounted for.
Kirchhoff’s Rules
• Junction Rule: The total current coming into a junction in a
circuit must equal the total current leaving that junction.
Σ Iin = Σ Iout
• Loop Rule: For any close-circuit loop (path), the sum of all
the potential (voltage) drops must equal the sum of all the
potential (voltage) gains.
Δ Vloop= Σ Vi = 0
Kirchhoff’s Loop Law
Slide 23-16
Resistors in Series
• For resistors in series, the total or equivalent resistance (of
the combo) is simply the sum of the individual resistances:
RS = R1 + R2 + R3 + ….
• The equivalent resistance is the same as the one resistance
that could replace all the other resistors and still have the
same current through that part of the circuit.
• Each resistor must have the same current, I.
Resistors in Series (continued)
• The voltage drop across each resistor is V = IR.
• The voltage drop across the combo of resistors is the sum of
the individual voltage drops and is equal to current times
the equivalent resistance, RS.
Vtotal = V1 + V2 + V3 +… = I RS
• The power dissipated through each resistor is P = I2 R.
• The total power dissipated through the combo of resistors is
equal to the sum of the power dissipated through the
individual resistors and is equal to the power dissipated
through an equivalent resistor, RS.
Ptotal = P1 + P2 + P3 +… = I2 RS
Resistors in Parallel
• For resistors in parallel, the total or equivalent resistance
(of the combo) is the reciprocal of the sum of the reciprocals
of the individual resistances:
1 / RP = 1 / R1 + 1 / R2 + 1 / R3 + ….
• The equivalent resistance is the same as the one resistance
that could replace all the other resistors and still have the
same current through that part of the circuit.
• Note that the equivalent resistance will be less than the least
of the individual resistors.
• Each resistor must have the same potential drop or voltage.
Resistors in Parallel (continued)
• The current through each resistor is I = V / R.
• The current through all of the resistors is the sum of the
individual currents and is equal to voltage divided by the
equivalent resistance, RP.
Itotal = I1 + I2 + I3 +… = V / RP
• The power dissipated through each resistor is P = I2 R.
• The total power dissipated through the combo of resistors is
equal to the sum of the power dissipated through the
individual resistors and is equal to the power dissipated
through an equivalent resistor, RP.
Ptotal = P1 + P2 + P3 +… = I2 RP
Household Circuits
• The outlets and most lighting in your house are wired in
parallel. How do you know?
- Everything has the same voltage.
- One thing turned off doesn’t affect other things.
- Note that switches must be wired in series with the
outlets or lights they control.
- Circuit breakers/fuses must also be in series with the
circuit they are designed to protect.
Resistors in Both Series and Parallel
• Woohoo!
• If too complex, need Kirchhoff’s Rules and a “system”.
• For simpler circuits (mostly resistors in series and parallel
with one battery), simplify and “piece together” the
solution.
• Do lots of examples. Here’s one.
Solving Circuits with Kirchhoff’s Rules
• Draw out the circuit.
• Draw the current in each branch of the circuit. Generally, in
the direction you believe the current goes, but, the direction
is arbitrary. If you choose incorrectly, your calculations will
result in a negative value, meaning the correct direction is
opposite your chosen direction.
• Mark each resistor end with a plus and minus sign, based on
your chosen current direction. Outside of a battery, current
always flows from higher (+) potential to lower (-) potential
• Apply the junction rule at all junctions.
Solving Circuits with Kirchhoff’s Rules (continued)
• Assign loop directions for each loop. Direction is arbitrary;
you’ll get the same (correct) answer either way. Generally,
loop from – to + through batteries when possible. This is for
intuition’s sake and isn’t necessary.
• Apply the loop rule going in the direction chosen.
Σ Vdrops = Σ Vrises
Potential in resistors is given by Ohm’s Law, V=IR.
Potential in batteries is given by size of battery.
Solving Circuits with Kirchhoff’s Rules (continued)
• Looping rule continued:
Looping through any device from + to – is a Vdrop.
Looping through any device from – to + is a Vrise.
A loop that goes against the current in a resistor signifies a
potential rise, Vrise.
• Obtain as many equations as unknowns.
• Solve equations simultaneously.
• Check.
Double-check potential sum in loop.
Check if/that Pinput = Poutput.
Internal Resistance and Terminal Voltage
• Devices that provide emf, batteries and generators for example, also
have their own internal resistance.
• This resistance can be thought of as a separate resistor in series with
the device and the circuit.
• This lowers the output voltage from its nominal value.
• The output voltage is called the terminal voltage (since it’s measured
at the terminals.) It’s dependent on the total current being drawn from
the source (battery).
Vterminal = E – I Rinternal
• A voltmeter might register adequate voltage (emf), but, a voltmeter
draws little/no current. The battery looks good, but, when current is
drawn from battery, the terminal voltage drops to low levels.
• This is why the best battery test is a load test.
Capacitors in Series and Parallel
• For capacitors in series and parallel, the add-em-up-rules
are opposite from those for resistors.
• For capacitors in series, the total or equivalent capacitance
(of the combo) is the reciprocal of the sum of the reciprocals
of the individual capacitances:
1 / CS = 1 / C1 + 1 / C2 + 1 / C3 + ….
• For capacitors in parallel, the total or equivalent
capacitance is the sum of the individual capacitances:
CP = C1 + C2 + C3 + ….