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Correct answer: 5 amp

Power dissipated in a resistive load is given by:

\[ P = I^2 R \]

Solving for current:

\[ I = \sqrt{\frac{P}{R}} \]

Given:

• \(P = 500\ \mathrm{W}\)
• \(R = 20\ \Omega\)

Substituting:

\[ I = \sqrt{\frac{500}{20}} = \sqrt{25} = 5\ \mathrm{A} \]

• 25 amp would correspond to a much higher power for a 20 \(\Omega\) load.
• 2.5 amp would only deliver \(P = (2.5)^2 \times 20 = 125\ \mathrm{W}\).
• 10 amp would deliver \(P = (10)^2 \times 20 = 2000\ \mathrm{W}\).

Therefore, the antenna current is 5 amp.

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Correct answer: 24 watt

Three equal resistors in parallel share the load, so the equivalent resistance is:

\[ R_{eq} = \frac{18\ \Omega}{3} = 6\ \Omega \]

Using the power formula:

\[ P = \frac{V^2}{R} \]

Substituting \(V = 12\ \mathrm{V}\) and \(R = 6\ \Omega\):

\[ P = \frac{12^2}{6} = \frac{144}{6} = 24\ \mathrm{W} \]

• 3 watt is far too small for a 12 V supply across a low resistance.
• 18 watt would correspond to a higher equivalent resistance than calculated.
• 36 watt would require an even lower equivalent resistance.

Therefore, the total power dissipation of the resistor load is 24 watt.

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By convention, \(P\) is power, \(I\) is current, \(R\) is resistance, and \(E\) is Voltage (Electro-motive force).

The Power Law states: \(P = I \times E\). Ohm's law states that \(E = I \times R\). Combining those to remove E, we get a restatement of the Power Law as \(P = I \times (I \times R)\), or \(P = I^2 \times R\)

So in this case:

\[P = (.02)^2 \times 10,000\] \[P = 0.0004 \times 10,000\]

Thus

\[P = 4 \text{ watts}\]

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Correct answer: increase by four times

For a fixed total resistance, electrical power is related to voltage by:

\[ P = \frac{V^2}{R} \]

If the applied voltage is doubled from \(V\) to \(2V\), the new power becomes:

\[ P_{new} = \frac{(2V)^2}{R} = \frac{4V^2}{R} = 4P \]

So the total power dissipated increases by a factor of four.

• decrease to half is incorrect because increasing voltage increases power.
• double would only occur if power were directly proportional to voltage, which it is not.
• not change is incorrect because power depends on the square of the voltage.

Therefore, doubling the applied voltage causes the total power dissipated to increase by four times.

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