Practice Problems (KEY)

Practice Problems (KEY)#

For the circuit below, find the source RMS voltage, the turns ratio for the transformer, and the power produced by the source.

\[ V_{S,RMS} = \frac{V_{S,pk}}{\sqrt{2}} = \frac{120}{\sqrt{2}} = 84.85\ \mathrm{V} \]
\[ a = \frac{V_{1}}{V_{2}} = \frac{120}{8} = 15 \]
\[ P_{payload} = IV = (6)(20) = 120\ \mathrm{W} \]
\[ \eta = \frac{P_{out}}{P_{in}} \cdot 100, \qquad P_{in} = \frac{P_{out}}{\eta} = \frac{120\ \mathrm{W}}{0.9} = 133\ \mathrm{W} \]

  1. What is the source current and turns ratio of the transformer?

\[ a = \frac{V_{1}}{V_{2}} = \frac{120}{24} = 5 \]
\[ P_{load} = IV = (6)(15) = 90\ \mathrm{W} \]
\[ \eta = \frac{P_{out}}{P_{in}} \cdot 100, \qquad P_{in} = \frac{P_{out}}{\eta} = \frac{90\ \mathrm{W}}{0.75} = 120\ \mathrm{W} \]
\[ I_{S} = \frac{P_{in}}{V_{S}} = \frac{120\ \mathrm{W}}{120\ \mathrm{V}} = 1\ \mathrm{A} \]

  1. You want to plug a device with an ADC into the wall socket. The ADC requires
    \(V_{in} = 30\ \mathrm{V}_{RMS}\). Your group determines that you need to put something in to reduce the voltage before it gets to the ADC. One design partner thinks you need to add a resistive voltage adapter. The other says you should use a transformer in the circuit. Which option is right and why?

This circuit is an AC circuit and can be used with a transformer. Voltage adapters are used to change voltages in a DC circuit, while transformers are used in AC circuits. You should use a transformer because it is more efficient than a voltage adapter.

We used voltage adapters in Block 1 to get the correct voltage across a device. In using them, we found the voltage drop needed across the device with KVL. After finding the voltage drop, we calculated the current through the voltage adapter, which allowed us to calculate the resistance using Ohm’s law. Since voltage adapters are resistive devices with voltages and currents, they consume power, resulting in power losses that are not useful. For this reason, voltage adapters cannot be 100% efficient, whereas transformers are treated as 100% efficient in this class.

Transformers will always be more efficient than voltage adapters, but remember that transformers can only be used with AC power. Voltage adapters, on the other hand, can be used with both AC and DC power.

  1. What is a semiconductor device that allows current to flow in only one direction?

a. Diode
b. Capacitor
c. Circuit breaker
d. Transistor

  1. What does a capacitor do in an AC-to-DC converter?

a. Eliminates the bias
b. Kills the negative voltage
c. Smooths the output
d. Protects the circuit