Question

From the combination of resistors with resistance values $ R_1 = R_2 = R_3 = 5 \, \Omega $ and $ R_4 = 10 \, \Omega $, which of the following combination is the best circuit to get an equivalent resistance of 6 $ \Omega $?

• A.
• B.
• C.
• D.

Hint:

To achieve the required equivalent resistance, combine resistors in series and parallel according to the desired total resistance.

Answer 1

The Correct Option is A

To find the best combination of resistors with given resistance values to obtain an equivalent resistance of 6 Ω, let's analyze each configuration option:

1. Observe that we have resistors: \( R_1 = R_2 = R_3 = 5 \, \Omega \) and \( R_4 = 10 \, \Omega \).
2. The task demands achieving an equivalent resistance of 6 Ω using these resistors.
3. The provided correct circuit looks something like this:
4. The solution involves using the electrical arrangement via series and parallel combinations:
5. Specifically, when resistors \( R_1 \), \( R_2 \), and \( R_3 \) are connected in parallel:
6. Next, connect \( R_4 = 10 \, \Omega \) in series with the calculated \( R_{\text{parallel}} \).
7. The total resistance is thus calculated as:

On comparing and rechecking, if using these configurations won't yield 6.0 Ω, the depicted combination below potentially showcases the expected correct selection. Ensure to replicate these equations to sync with unit transformation or specific solution context:

Answer 2

The equivalent resistance of resistors in series and parallel is calculated using the following formulas:
1. Resistors in Series: \[ R_{\text{eq}} = R_1 + R_2 + \dots \]
2. Resistors in Parallel: \[ \frac{1}{R_{\text{eq}}} = \frac{1}{R_1} + \frac{1}{R_2} + \dots \]
Using the correct combination, it is found that the first option gives the desired equivalent resistance of \( 6 \, \Omega \).
Thus, the correct answer is (1).