Question

\(4 \Omega, 8 \Omega, R\) resistors are connected in series. Resultant resistance is \(20 \Omega\). Then \(R=?\)

• A. \(6 \Omega\)
• B. \(4 \Omega\)
• C. \(18\Omega\)
• D. \(8 \Omega\)

Answer 1

The Correct Option is D

To solve the problem, we need to find the unknown resistance \( R \) when three resistors are connected in series and the total resistance is given.

1. Understanding Series Connection:
In a series connection, the total or resultant resistance \( R_{\text{total}} \) is the sum of all individual resistances:

\[ R_{\text{total}} = R_1 + R_2 + R_3 \]

2. Substitute the Known Values:
Given: \( R_1 = 4\, \Omega \), \( R_2 = 8\, \Omega \), and \( R_3 = R \)
Also, \( R_{\text{total}} = 20\, \Omega \)

\[ 4 + 8 + R = 20 \]

3. Solve for R:
\[ 12 + R = 20 \Rightarrow R = 20 - 12 = 8\, \Omega \]

Final Answer:
The correct answer is option (D): 8 Ω.