A capacitor is sometimes placed in series with the primary of a power transformer to:

Improve the power factor

The capacitor stores electrical current in an electrical field. It helps to control the flow of the current, though passively.

For AC circuit, the ratio of average power to the apparent power is called the power factor. The apparent power is derived from the multiplication of the current level and voltage.

The power factor, called PF, is the working power expressed in kilowatts, or kW, and the apparent power expressed in kilovolt amperes, or kVA.

See Wikipedia's article on Capacitor, and also an article on the Power Factor.

For more information, please see All About Circuits site for the article Calculating Power Factor.

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A transformer used to step up its input voltage must have:

More turns of wire on its secondary than on its primary.

From sammylandler.:

When the power is the same, voltage and current are inversely proportional. Transformers can be used to increase the voltage in an AC circuit at the expense of current and vice versa.

A transformer has a core and two wires wrapped around opposite ends of the core.

If the primary winding (source) has more turns than the secondary winding (load), then the voltage will decrease and the current will increase.

However, if the primary winding has fewer turns than the secondary winding, the voltage will increase and the current will decrease.

Please see Wikipedia's article on Transformers

Also, see the Electronics Tutorials site for the well-illustrated article called Transformer Basics

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A transformer primary of
2250 turns connected to
120 VAC will develop what voltage across a
500-turn secondary?

26.7 volts.

From kd7bbc:

Solve for \(X\)

\[\begin{align} 2,250 \text{ turns} &= 120 \text{ volts} \\ 500 \text{ turns} &= X \\ 120\text{ volts} \times 500\text{ turns} &= 60,000 \\ \frac{60,000}{2,250} &= 26.666....... \\ X &= 26.7\text{ Volts} \end{align}\]

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What is the ratio of the output frequency to the input frequency of a single-phase full-wave rectifier?

2:1.

From chris.melchior.:

In the AC voltage, the rectifier is turning both the positive and negative pulses of the sine waves into positive pulses only.

This, effectively doubles the original positive pulse frequency. So, what was typically 60 Hz now would become 120 Hz.

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A power transformer has a single primary winding and three secondary windings producing
5.0 volts,
12.6 volts, and
150 volts.

Assuming similar wire sizes, which of the three secondary windings will have the highest measured DC resistance?

The 150 volt winding.

The more volts winding the bigger the DC resistance. Size does matter here.

From kd7bbc:

The ratio between the secondary voltage and primary voltage is the same as the ratio of the secondary winding to the primary winding, so:

\[\frac{\text{Windings}_\text{secondary}}{\text{Windings}_\text{primary}} = \frac{V_{\text{secondary}}}{V_{\text{primary}}}\]

or

\[\frac{\text{Windings}_\text{secondary}}{\text{Windings}_\text{primary}} \times V_{\text{primary}} = V_{\text{secondary}}\]

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A power transformer has a primary winding of
200 turns of #24 wire
and a secondary winding consisting of
500 turns of the same size wire.

When 20 volts are applied to the primary winding, the expected secondary voltage will be:

50 volts.

From kd7bbc:

The ratio between the secondary voltage and primary voltage is the same as the ratio of the secondary winding to the primary winding, so:

\[\frac{\text{Windings}_\text{secondary}}{\text{Windings}_\text{primary}} = \frac{V_{\text{secondary}}}{V_{\text{primary}}}\]

or

\[\frac{\text{Windings}_\text{secondary}}{\text{Windings}_\text{primary}} \times V_{\text{primary}} = V_{\text{secondary}}\]

so if we substitute, we get:

\[\frac{500}{200} \times 20 = 50 V\]

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