Answer Key: Electrical Theory Practice¶
Schematic Symbols¶
Please write one or more names of the component or concept represented by each schematic symbol below. For some cases several hand-drawn variants are included.
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Any of the following answers is acceptable:
resistor
voltage source, power supply, +5V supply, +9V supply
ground, 0 Volts
battery, 9V battery
LED, light-emitting diode. (Not ‘lamp’ or ‘light’).
switch, momentary-contact switch, SPST switch, SPDT switch, toggle switch
potentiometer, variable resistor
photocell, photoresistor, CdS cell
speaker
MOSFET, N-channel MOSFET
transistor, bipolar transistor, NPN transistor, PNP transistor
relay
What is the meaning of each of the following acronyms?
Acronym |
Meaning |
---|---|
SPST |
single-pole single-throw (applied to a switch) |
SPDT |
single-pole double-throw (applied to a switch) |
LED |
light-emitting diode |
DMM |
digital multi-meter |
Please label the anode and cathode on the following.
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Is the anode or cathode the more positive terminal when the device is conducting?
Anode
Notation¶
What property and measurement units do each of the following symbols typically represent?
Symbol |
Property |
Units |
---|---|---|
i |
current |
Ampere, milliAmperes |
V |
voltage |
Volt |
R |
resistance |
Ohm, kilo-Ohm |
What do each of these symbols indicate on a schematic?
Symbol |
Meaning |
---|---|
Ω |
Ohms |
K |
kilo-Ohms |
Rules and Measurement¶
If a voltage V is measured between two nodes, what is the measurement if the leads are reversed?
−VWhat is the canonical form of Ohm’s Law? What are the alternate forms that solve for each dependent variable?
V=iRi=V/RR=V/iWhat is a concise mathematical statement that can be made about the sum of currents entering a given node?
The currents entering a node sum to zero:
∑in=0What is a concise mathematical statement that can be made about the sum of voltages around a circuit loop?
The sum of potentials around a loop is zero:
∑vn=0If voltage Vxy is measured between points X and Y, and voltage Vyz between points Y and Z, what is the voltage Vxz between points X and Z?
Vxz=Vxy+Vyz
Circuits¶
Please determine the specific quantities requested for each circuit. Please be sure to include correct units.
Note: each answer below suggests an analysis at a pragmatic level for this course. These are by no means the only approaches.
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What is the value of i?
This is a plain application of Ohm’s Law:
i=V/R=5/10000=0.0005A=0.5mA
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What are the values of i and V?
If you apply the heuristic that resistances in series add:
i=V/(R1+R2)=5/20000=0.25mA
The voltage drop across the lower resistor comes from Ohm’s Law:
V=iR=0.25mA∗10000=2.5V
Fully solving this using only Ohm’s Law is identical to proving the formulas for a voltage divider.
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What is the value of R?
Loop voltages must sum to zero, so the potential across the resistor:
Vr=5−1.6=3.4V
The resistor value is a plain application of Ohm’s Law:
R=V/i=3.4/i
That’s as much as can be said without a specific value of i. But a typical LED current can run as high as 20 mA, so a reasonable answer could be:
R=3.4/0.020=170Ω
This represents a lower bound on reasonable values; lower resistances will allow too much current through the LED, higher values will run it dimmer with more safety margin.
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What is the value of i?
Each resistor has a current according to Ohm’s Law:
ir=V/R=5/10000=0.5mA
The input current is the sum of the two resistor currents:
i=ir1+ir2=0.5+0.5=1.0mA
Formally, the resistor currents have negative sign with respect to the node, and the currents sum to zero:
i+ir1+ir2=0i+(−0.5mA)+(−0.5mA)=0i=1.0mA
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What is the value of R for which the component on the right is equivalent to the circuit on the left?
Following on the previous example:
R=V/iR=5/0.001AR=5000ΩR=5KThe general formula for the combined resistance of two resistors in parallel is:
R=(R1R2)/(R1+R2)
If the two values are equal, this reduces:
R=(RnRn)/(2Rn)R=Rn/2