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: Equivalent Resistance Formula (Parallel)
For resistors in parallel, the reciprocal of the equivalent resistance \( R_{eq} \) is calculated as:\[\frac{1}{R_{eq}} = \frac{1}{R_1} + \frac{1}{R_2}\]
Step 2: Input Resistance Values
Given:- \( R_1 = 5 \, \Omega \)- \( R_2 = 10 \, \Omega \)Substitute these values into the formula:\[\frac{1}{R_{eq}} = \frac{1}{5} + \frac{1}{10} = \frac{2}{10} + \frac{1}{10} = \frac{3}{10}\]
Step 3: Compute Equivalent Resistance
Invert the result to find \( R_{eq} \):\[R_{eq} = \frac{10}{3} = 3.33 \, \Omega\]
Conclusion:
The combined equivalent resistance is \( 3.33 \, \Omega \). This corresponds to option (1).