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: Determine total resistance required at minimum current.
Minimum desired current is
\[ I_{\min} = 3 \text{ A} \]
Using Ohm’s law,
\[ R_{\text{total,max}} = \frac{V}{I_{\min}} = \frac{120}{3} = 40 \, \Omega \]
Step 2: Calculate maximum rheostat resistance.
Load resistance is
\[ R_L = 10 \, \Omega \]
Hence, rheostat resistance required is
\[ R_{\text{rheostat,max}} = 40 - 10 = 30 \, \Omega \]
Step 3: Determine total resistance required at maximum current.
Maximum desired current is
\[ I_{\max} = 5 \text{ A} \]
\[ R_{\text{total,min}} = \frac{120}{5} = 24 \, \Omega \]
Step 4: Check rheostat range.
At maximum current, rheostat resistance is
\[ R_{\text{rheostat,min}} = 24 - 10 = 14 \, \Omega \]
Thus, the rheostat must be capable of varying resistance approximately between $14 \, \Omega$ and $30 \, \Omega$.
Step 5: Select nearest standard option.
From the given choices, the suitable rheostat is
\[ \boxed{20 \, \Omega \text{ with a current rating of } 10 \text{ A}} \]
Step 6: Current rating justification.
The rheostat must safely carry the maximum current of $5 \, \text{A}$, hence a $10 \, \text{A}$ rated rheostat is appropriate.