# Transformers and Impedance Matching

• mikejones2000
In summary, the conversation involved various homework problems related to resistors, capacitors, inductors, transformers, and solar energy. The solutions involved using equations to calculate voltage drops, power, impedance ratios, and energy absorption. One problem involved an error in the question regarding the output impedance of an amplifier. Another problem involved a typo in the units for solar radiation intensity. In the end, the solution for the problem involving solar energy required multiplying various values and taking into account the angle of elevation and the area of the beach blanket.
mikejones2000
Hey all, any help with any of these problems would be greatly appreciated, I have attempted all but one(because I do not even know where to start).

## Homework Statement

A 58.0 resistor, a 3.00 µF capacitor, and a 0.400 H inductor are connected in series to a 77.0 V (rms), 60.0 Hz source.
(a) Find the voltage drop across the LC combination.
(b) Find the voltage drop across the RC combination.

## Homework Equations

For RC-> Z=sqr(R^2+Xc^2), Vmax=ImaxZ, For LC-> Z=sqr(R^2+(Xl-Xc)^2), I=V/R, Vmax=V(sqr(2)).

## The Attempt at a Solution

I calculated Imax first and then found each different Z. I then put the values into Vmax=ImaxZ.

## Homework Statement

An AC adapter for a telephone-answering unit uses a transformer to reduce the line voltage of 120 V (rms) to a voltage of 9.5 V. The rms current delivered to the answering system is 390 mA.
(a) If the primary (input) coil in the transformer in the adapter has 240 turns, how many turns are there on the secondary (output) coil?
(b) What is the rms power delivered to the transformer? Assume an ideal transformer.

## Homework Equations

Vc=(N2/N1)V1, Pav=IrmsVr

## The Attempt at a Solution

I know how to get the first part of this question but the second eludes me. I tried using 120V for Vr and also 120(sqr(2)) considering the transformer is ideal.

## Homework Statement

Suppose you wish to use a transformer as an impedance-matching device between an audio amplifier that has an output impedance of 6.8 k and a speaker that has an input impedance of 6.5 . What should be the ratio of primary to secondary turns on the transformer?

## Homework Equations

I could not find any equations relating impedance and transformers in my text but I found one online->Z1/Z2=(N1/N2)^2

## The Attempt at a Solution

Plug'chugged and got it wrong. :(

## Homework Statement

The intensity of solar radiation at the top of Earth's atmosphere is 1340 W/m3. Assuming that 60% of the incoming solar energy reaches Earth's surface and assuming that you absorb 50% of the incident energy, make an order-of-magnitude estimate of the amount of solar energy you absorb in a 60 minute sunbath. (Assume that you occupy a 1.7 m by 0.3 m area of beach blanket and that the sun's angle of elevation is 60°.)

## The Attempt at a Solution

I am rather clueless at where to begin with this one. I understand that the energy will be reduced by .6 and then by .5 but I am pretty stumped.

*A* I'd start by calculating the total complex impedance of the series RLC combination, and using that to calculate the complex current. Once you have the current, then you can do the impedance combinations to get the individual voltage drops. Your way may work as well, but I didn't understand it with a quick read.

*B* Hopefully the question says 9.5Vrms output? For the calc (b), remember that for an ideal transformer, primary power in = secondary power out. You are given the primary input voltage and primary input current, so what can you say about the output power and current?

*C* Check the problem statement. I think it is a typo to say that the audio output amplifier has an output impedance of 6.8kOhms... are you sure? That's pretty high for any kind of amp to feed a speaker, even a small one. That's probably where the error is. And yes, that is the correct equation. But before just using it, you should understand how to derive it. What is the relationship between input/output voltages in terms of number of turns? What is the similar relationship between input/output currents in terms of number of turns. Now, remembering that Z=V/I, what can you say about the transformed impedance ratio looking through a transformer at a secondary load...?

*D* Hint -- Watt is a measure of power. Joule is a measure of energy. What is the relationship that relates power to energy?

(whew, my fingers are tired!)

Ok, I resolved all of the problems except this one:
The intensity of solar radiation at the top of Earth's atmosphere is 1340 W/m3. Assuming that 60% of the incoming solar energy reaches Earth's surface and assuming that you absorb 50% of the incident energy, make an order-of-magnitude estimate of the amount of solar energy you absorb in a 60 minute sunbath. (Assume that you occupy a 1.7 m by 0.3 m area of beach blanket and that the sun's angle of elevation is 60°.)
DeltaE = 10___

Solution: I multiplied the intensity by .5 and .6. I then multiplied that number by (1.7 * .3)(60 minutes * 60 seconds). I then multiplied it by cos60 and sin60 but still did not get a correct answer. Any quick response/help would be greatly appreciated, the homework is due soon. Thanks in advance, Mike.

What did you get? The sin(60 degrees) answer is preferable, since that's the correct choice. The more work you can show us the easier to tell where you might have gone wrong. If anywhere. Note the questions asks for 'order of magnitude' (just a power of 10?).

## 1. What is alternating current (AC) and how is it different from direct current (DC)?

Alternating current is a type of electrical current in which the direction of flow of electrons periodically reverses. This is in contrast to direct current, which flows in only one direction. AC is used for power transmission over long distances and is more commonly used in household appliances.

## 2. What are the common problems associated with alternating current?

Some common problems associated with alternating current include voltage drops, power surges, and electrical noise. These issues can lead to equipment failure, power outages, and other electrical problems.

## 3. How can voltage drops be prevented in an AC circuit?

One way to prevent voltage drops in an AC circuit is by using thicker wires with lower resistance. Another method is to use voltage regulators or stabilizers to maintain a constant voltage level.

## 4. What causes power surges in an AC circuit?

Power surges in an AC circuit can be caused by lightning strikes, faulty wiring, or sudden changes in the flow of electricity. They can also be caused by large appliances turning on and off, causing a spike in the electrical current.

## 5. How can electrical noise be reduced in an AC circuit?

Electrical noise, also known as interference, can be reduced in an AC circuit by using filters and shielding on electronic devices. Proper grounding and using twisted pair wiring can also help reduce noise. In addition, keeping devices away from sources of interference, such as motors or fluorescent lights, can also help reduce noise.

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