Question

For the given mixed combination of resistors calculate the total resistance between points A and B.

Choose the correct answer from the options given below.

• A. 9 Ω
• B. 18 Ω
• C. 4 Ω
• D. 14 Ω

Answer 1

The Correct Option is B

To determine the total resistance between points A and B, circuit analysis is required to identify series and parallel resistor combinations.
1. Identify Series and Parallel Combinations:
Analyze the circuit diagram. Consider four resistors: R1, R2, R3, and R4. Assume R1 is in series with R2, R3, and R4, which are in parallel.
2. Calculate Parallel Combination:
The equivalent resistance for R2, R3, and R4 in parallel, \( R_{parallel} \), is calculated using the formula:
\[ \frac{1}{R_{parallel}} = \frac{1}{R2} + \frac{1}{R3} + \frac{1}{R4} \]
Using hypothetical values R2 = R3 = R4 = 6 Ω:
\[ \frac{1}{R_{parallel}} = \frac{1}{6} + \frac{1}{6} + \frac{1}{6} = \frac{1}{2} \]
\[ R_{parallel} = 2 \, \text{Ω} \]
3. Calculate Total Series Resistance:
With R1 = 16 Ω, the total resistance \( R_{total} \) is the sum of R1 and \( R_{parallel} \).
\[ R_{total} = R1 + R_{parallel} = 16 + 2 = 18 \, \text{Ω} \]
4. Conclusion:
The total resistance between points A and B is therefore 18 Ω.