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.
![../../../_images/schematic-symbols.png](../../../_images/schematic-symbols.png)
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.
![../../../_images/anode-cathode.png](../../../_images/anode-cathode.png)
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 |
---|---|
\(\Omega\) |
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?
\(-V\)What is the canonical form of Ohm’s Law? What are the alternate forms that solve for each dependent variable?
\(V = iR\)\(i = V/R\)\(R = V/i\)What 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:
\(\sum i_n = 0\)What 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:
\(\sum v_n = 0\)If voltage \(V_{xy}\) is measured between points X and Y, and voltage \(V_{yz}\) between points Y and Z, what is the voltage \(V_{xz}\) between points X and Z?
\(V_{xz} = V_{xy} + V_{yz}\)
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.
![../../../_images/circuit1.png](../../../_images/circuit1.png)
What is the value of \(i\)?
This is a plain application of Ohm’s Law:
\(i = V / R = 5 / 10000 = 0.0005 A = 0.5 \mathrm{mA}\)
![../../../_images/circuit2.png](../../../_images/circuit2.png)
What are the values of \(i\) and \(V\)?
If you apply the heuristic that resistances in series add:
\(i = V / (R1 + R2) = 5 / 20000 = 0.25 \mathrm{mA}\)
The voltage drop across the lower resistor comes from Ohm’s Law:
\(V = i R = 0.25 \mathrm{mA} * 10000 = 2.5V\)
Fully solving this using only Ohm’s Law is identical to proving the formulas for a voltage divider.
![../../../_images/circuit3.png](../../../_images/circuit3.png)
What is the value of \(R\)?
Loop voltages must sum to zero, so the potential across the resistor:
\(V_r = 5 - 1.6 = 3.4V\)
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:
\(R = 3.4 / 0.020 = 170 \Omega\)
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.
![../../../_images/circuit4.png](../../../_images/circuit4.png)
What is the value of \(i\)?
Each resistor has a current according to Ohm’s Law:
\(i_r = V / R = 5 / 10000 = 0.5 \mathrm{mA}\)
The input current is the sum of the two resistor currents:
\(i = i_{r1} + i_{r2} = 0.5 + 0.5 = 1.0 \mathrm{mA}\)
Formally, the resistor currents have negative sign with respect to the node, and the currents sum to zero:
\(i + i_{r1} + i_{r2} = 0\)\(i + (-0.5 \mathrm{mA}) + (-0.5\mathrm{mA}) = 0\)\(i = 1.0 \mathrm{mA}\)
![../../../_images/circuit5.png](../../../_images/circuit5.png)
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:
\(R = V / i\)\(R = 5 / 0.001 \mathrm{A}\)\(R = 5000 \Omega\)\(R = 5\mathrm{K}\)The general formula for the combined resistance of two resistors in parallel is:
\(R = (R_1 R_2) / (R_1 + R_2)\)
If the two values are equal, this reduces:
\(R = (R_n R_n) / (2 R_n)\)\(R = R_n / 2\)