Controlling The Real World With Computers
::. Control And Embedded Systems .::

1. B) Schematic

2. D) Switch

3. A) Resistor

4. E) Ohm, B) Ohm's Law

5. A) Amperes (or Amps), E) Milliamps (or Ma or ma)

6. C) Capacitors

7. B) Diode

8. D) Integrated Circuits

9. B) Operational Amplifier

10. This shows unconnected conductors.

11. This is a resistor.

12. This is a switch.

13. This is connected conductors.

14. This is a capacitor.

15. This is a diode.

16. This is the symbol for ground.

17. Ohm's Law: V = IR

18. I = 4, R = 10 so V = IR = 40 Volts

19. V = 12, R = 6 so I = V/R = 2 Amps

20. I = 75, V = 150K Volts so R = V/I = 150K/75 = 2K Ohms

21. P = VI = 150K * 75 = 11,250,000 Watts

22. 25K ohms

So, the total resistance in the above circuit = 3000 ohms

Now, remember that the current in a circuit = I = V/R.

The voltage is 3 volts

So, remembering to write the equation first, plug in the values to get the current:

I = V/R = 3/3000 = 1 ma

Since all three resistors are 1000 ohms in the above circuit, there is a total of 3000 ohms, and I = 3/3000 = 1ma. Remember, ma means milliamps or thousandths of an amp, so 1ma is the same as 1/1000th of an amp. Now, to find the voltage across each 1K resistor, use V = IR.

So, the calculated voltage across each resistor =

V = IR = 1ma * 1000 = 1 volt

Would including a 10K resistor work? No, because that would make the whole circuit more than 10K ohms.

1,385,247 0 = 1 (anything raised to the power of 0 is 1)

1 X 103 = 1000 (any time you have 1 x 10 raised to a power, just write down 1, then the number of zeros indicated by the exponent – 3 in this case)

.1ma = 1/10000 amps (remember that ma means milliamps, and that mili means 1/1000th. This is 1/10th of that, which is 1/10000)

101 = 10 (anything raised to the power of 1 is itself)

10-4 = .0001 or 1/10000 (remember to start with a 1 followed by a decimal, then move the decimal to the left the number of places shown by the negative exponent)

For the number 432.178,

the 4 is in the 100 s place,

the 7 is in the 1/100 s place, and

the 8 is in the 1/1000 s place.

xy0 = x raised to the power of y which is raised to the power of 0 = x
Work from right to left: y raised to the power of 0 is 1, then x raised to the power of 1 is x.

From the parallel circuit problem: But since you know the voltage, you can use the rules for a parallel circuit and Ohm's law for resistance and current. So calculate the following. Remember, the voltage is 3 volts across each resistor. Also remember to write Ohm's law for current first, which is I = V/R :

Current through R1: I = V/R = 3/30K = .1 ma (.0001 amp)

Current through R2: I = V/R = 3/300 = .01 amp

Current through R3: I = V/R = 3/3K = 1 ma (.001 amp)

Total current through all 3 = 11.1 ma (.0111 amp)

Since you know the source voltage is 3 volts and you know the total current, you can calculate the combined resistance using Ohm's law for resistance, which is R=V/I :

Rtotal = R=V/I = 3/.0111 = 270.270 ohms rounded off

Notice that the resulting value is less than the lowest value in the circuit.
This means the answer is reasonable, since the parallel value must be less than the lowest value.