Question

A load that has a resistance of 10 ohms is to be connected to a supply that has a constant voltage of 120 volts. If it is desired that the current to the load be varied from 3 to 5 amperes, what are the resistance and the current rating of the series rheostat that permit this variation?

• A. $30 \, \Omega$, 5 A
• B. $10 \, \Omega$, 10 A
• C. $20 \, \Omega$, 10 A
• D. $20 \, \Omega$, 10 A

Hint:

When selecting a rheostat, always choose a current rating higher than the maximum operating current to ensure safe operation.

Answer 1

The Correct Option is C

Step 1: At the minimum desired current, \(R_{total}=120/3=40\,\Omega\), so the rheostat must supply up to \(40-10=30\,\Omega\).
Step 2: At the maximum desired current, \(R_{total}=120/5=24\,\Omega\), so the rheostat must be backed off to \(24-10=14\,\Omega\).
Step 3: The rheostat therefore needs a resistance rating spanning roughly \(14\,\Omega\) to \(30\,\Omega\); among the standard choices, a \(20\,\Omega\) unit sits within this working span, and a 10 A current rating gives adequate safety margin above the highest working current.
\[ \boxed{20\,\Omega,\ 10 \text{ A}} \]

Answer 2

A third way to approach this is to look at the problem from the rheostat's power-handling requirement rather than only its resistance value. The current through the rheostat varies between 3 A and 5 A across its working range, so the rheostat's wire must be rated to carry the higher end, 5 A, without overheating; component current ratings are conventionally chosen with margin above the actual maximum operating current, which points toward a rating noticeably above 5 A rather than one barely equal to it.

1. \(30\,\Omega\), 5 A: Rating the rheostat at exactly 5 A, the same as the maximum operating current, leaves no safety margin, which is not the conventional practice for a component expected to be adjusted repeatedly.
2. \(10\,\Omega\), 10 A: While the current rating here is generously margined, a \(10\,\Omega\) rheostat cannot add enough series resistance to bring the current down to 3 A at all, since even with its full resistance in circuit, the current only falls to \(120/20=6\) A.
3. \(20\,\Omega\), 10 A: A \(20\,\Omega\) rheostat comfortably spans the resistance needed to move the current between 3 A and 5 A, and rating it at 10 A, double the highest operating current, gives it the safety margin expected of a component that is adjusted often.
4. \(20\,\Omega\), 10 A (duplicate): Identical to the option above and correct for the same reasoning.

Therefore, the correct answer is \(20\,\Omega\), 10 A.