Question

A 5 $\Omega$ resistor and a 10 $\Omega$ resistor are connected in parallel. What is the equivalent resistance of the combination?

• A. \( 3.33 \, \Omega \)
• B. \( 15 \, \Omega \)
• C. \( 7.5 \, \Omega \)
• D. \( 2 \, \Omega \)

Hint:

Remember: For resistors in parallel, the equivalent resistance is always less than the smallest resistor.

Answer 1

The Correct Option is A

Step 1: Formula for equivalent resistance in parallel
When resistors are connected in parallel, the reciprocal of the equivalent resistance \( R_{eq} \) is given by: \[ \frac{1}{R_{eq}} = \frac{1}{R_1} + \frac{1}{R_2} \]
Step 2: Substitute the values of resistances
Given: - \( R_1 = 5 \, \Omega \) - \( R_2 = 10 \, \Omega \) \[ \frac{1}{R_{eq}} = \frac{1}{5} + \frac{1}{10} = \frac{2}{10} + \frac{1}{10} = \frac{3}{10} \]
Step 3: Calculate the equivalent resistance
\[ R_{eq} = \frac{10}{3} = 3.33 \, \Omega \]
Answer:
Therefore, the equivalent resistance of the combination is \( 3.33 \, \Omega \). So, the correct answer is option (1).