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Transcript
```ELEC 225
Circuit Theory I
Fall 2005
Review Topics for Exam #1
 The following is a list of topics that could appear in one form or another on the exam. Not all
of these topics will be covered, and it is possible that an exam problem could cover a detail not
specifically listed here. However, this list has been made as comprehensive as possible.
Basic definitions
-
dW
dq
voltage is “felt” in a circuit almost instantaneously after it is applied
dq
current = time rate of flow of charge: i 
dq
current can be relatively slow (mm/sec), but current begins to flow everywhere
almost instantaneously after a source is applied
conventional current is in direction of positive charge flow, but electrons (neg.
charge) actually flows through wires
voltage develops across devices
current flows through devices
dW dq dW
power: p  iv 

dq dt
dt
voltage = energy transferred per unit charge: v 
Basic units
- voltage (V)
- current (A)
- power (W)
- charge (C); 1 electron has a charge of −1.602 × 10−19 C
- energy (J)
Passive sign convention, Ohm’s law, and power calculations
- v = iR or v = −iR
- p = iv or p = −iv
- sign on right hand side depends on direction of current relative to polarity of voltage
- if p is positive, then power is absorbed (dissipated)
- if p is negative, then power is delivered (supplied)
- power delivered = power absorbed
Power calculations for resistors
v2
- p  i 2 R or p 
R
- power is always dissipated in resistors (p is always positive)
Ideal independent voltage sources
- maintains indicated voltage between its two terminals at all times
- current through source depends on external circuit only
- source has no resistance
- a short circuit can be represented by a voltage source of 0 V
1
Ideal independent current sources
- maintains indicated current through its branch at all times
- voltage across source depends on external circuit only
- source has no resistance
- an open circuit can be represented by a current source of 0 A
Possible contradictions involving ideal voltage and current sources
- two or more voltage sources of different values in parallel is meaningless
- two or more current sources of different values in series is meaningless
Dependent sources
- voltage-controlled voltage source: v  v x , where vx is a voltage elsewhere in ckt,
and  is a constant. Current through source depends on external ckt only.
- voltage-controlled current source: i  v x , where vx is a voltage elsewhere in ckt, and
 is a constant. Voltage across source depends on external ckt only.
- current-controlled current source: i  i x , where ix is a current elsewhere in ckt, and 
is a constant. Voltage across source depends on external ckt only.
- current-controlled voltage source: v  i x , where ix is a current elsewhere in ckt, and
 is a constant. Current through source depends on external ckt only.
Kirchhoff’s voltage law (KVL)
- simply a restatement of the law of conservation of energy in ckt terms
- voltages around any closed path must add to zero
- sum of voltages around loop = 0, or sum of voltage rises = sum of voltage drops
- voltage rises and drops can be given either positive or negative signs in KVL
equation, but must be consistent within a single KVL equation
- corollary: voltage between two points = sum of voltage drops and rises between
those two points
Kirchhoff’s current law (KCL)
- simply a restatement of the law of conservation of mass (charge) in ckt terms
- current flowing into/out of any region of circuit must add to zero, or sum of currents
entering = sum of currents leaving
- currents entering and leaving can be given either positive or negative signs in KCL
equation, but must be consistent within a single KCL equation
Series resistors
- all have the same current flowing through them, but different voltages across them
- Req  R1  R2    R N
- if one resistor is orders of magnitude larger than the rest, then Req ≈ that value
Parallel resistors
- all have the same voltage across them, but different currents through them
1
- Req 
1
1
1


R1 R2
RN
RR
- special case for only two resistors: Req  1 2
R1  R2
- if one resistor is orders of magnitude smaller than the rest, then Req ≈ that value
- equiv. resistance of any finite resistor value in parallel with infinity = the finite value
Conductance (G; unit is Siemens, S or mho)
2
Voltage divider
- formed by two or more resistors in series (all must share the same current)
- let total voltage across entire set of resistors = vtot
- let voltage across kth resistor = vk
Rk
- vk 
vtot
R1  R2    RN
Current divider
- formed by two or more resistors in parallel (all must share the same voltage)
- let total current flowing into network of resistors = itot
- let current flowing through kth resistor = ik
Req
- ik 
itot
Rk
R2
R1
- special case for only two resistors: i1 
itot and i2 
itot
R1  R2
R1  R2
Basic nodal analysis
- based on KCL applied to all nodes except reference node
- definition of node: not just a “dot;” includes wires connected to dot(s)
- definition of node voltage: voltage measured between a node and the reference node
(ground); pos. side at node, neg. side at ground
- express currents flowing through resistors in terms of node voltages (use Ohm’s law)
- N nodes lead to N−1 independent equations
- equations should have only node voltages as unknowns
- solution of system of simultaneous equations required (for N nodes, it’s N−1 eqns in
N−1 unknowns)
Relevant course material:
HW:
Labs:
Textbook:
#1-#4
#1-#2
Chap. 1, Chap. 2, Secs. 3.1-3.4, Secs 4.1-4.4
3
```