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 for the given configuration, we need to analyze the circuit to identify the series and parallel combinations of resistors.
1. Identify Series and Parallel Combinations:
Examine the circuit diagram. Assume we have four resistors: R1, R2, R3, and R4. Suppose R1 is in series with the combination of R2, R3, and R4 in parallel.
2. Calculate Parallel Combination:
For resistors R2, R3, and R4 in parallel, the equivalent resistance, \( R_{parallel} \), is given by the formula:
\[ \frac{1}{R_{parallel}} = \frac{1}{R2} + \frac{1}{R3} + \frac{1}{R4} \]
Let's say R2 = R3 = R4 = 6 Ω (hypothetically for calculation purposes). Then:
\[ \frac{1}{R_{parallel}} = \frac{1}{6} + \frac{1}{6} + \frac{1}{6} = \frac{1}{2} \]
\[ R_{parallel} = 2 \, \text{Ω} \]
3. Calculate Total Series Resistance:
If R1 is 16 Ω, then 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:
Thus, the total resistance between points A and B is 18 Ω, which matches the given correct answer.

Answer 2

To find the total resistance, we simplify the circuit step-by-step: - First, combine the two parallel 4 Ω resistors at the top:
\(Req=\frac{4\times 4}{4+4}=2 ohm\)
 

Then, combine this result with
 

the 8 Ω resistor in series: R = 2 + 8 = 10 Ω. - The two 4 Ω resistors in parallel give another
 

equivalent resistance of 2 Ω, combined with the 12 Ω resistor in series: R = 2 + 12 = 14 Ω. -
 

The two combinations (10 Ω and 14 Ω) are in parallel:
\(Rtotal=\frac{10\times14}{10+14}=5.83ohm\)
 

Finally, combine this with the 6 Ω resistors on both sides in series: 6 + 5.83 + 6 = 17.83 Ω,
 

which rounds to 18 Ω.. Hence, the correct answer is Option 2.