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 determine the optimal resistor combination for a target equivalent resistance of 6 Ω, consider the following analysis of each configuration option:

1. Given resistors are: \( R_1 = R_2 = R_3 = 5 \, \Omega \) and \( R_4 = 10 \, \Omega \).
2. The objective is to achieve an equivalent resistance of 6 Ω using these specified resistors.
3. The validated circuit configuration is depicted below:
4. The solution employs a combination of series and parallel resistor arrangements.
5. Specifically, the parallel combination of resistors \( R_1 \), \( R_2 \), and \( R_3 \) is calculated first:
6. Subsequently, resistor \( R_4 = 10 \, \Omega \) is connected in series with the resultant parallel resistance, \( R_{\text{parallel}} \).
7. The total equivalent resistance is then computed as follows:

Upon review, if the aforementioned configurations do not result in 6.0 Ω, the circuit diagram provided below may represent the intended correct configuration. Verify these equations to ensure consistency with unit conversions or the specific context of the solution: