We have three resistances of values 2 Ω, 3 Ω and 6 Ω. Which of the following combination will give a

Question

We have three resistances of values 2 Ω, 3 Ω and 6 Ω. Which of the following combination will give an effective resistance of 4 Ω?

Examoogle · Accepted Answer

$2 \Omega$ resistance in series with parallel combination of $3 \Omega$ and $6 \Omega$ resistance

Explanation: Given: Three resistors with values R1 = 2 Ω, R2 = 3 Ω, and R3 = 6 Ω.

Formula Used: $$R_{eq} = R_s + \frac{R_p1 	imes R_p2}{R_p1 + R_p2}$$

Steps: Analyze the combination in Option B: According to option B, we have a $2 \Omega$ resistor in series with the parallel combination of $3 \Omega$ and $6 \Omega$ resistors.. Calculate equivalent resistance of parallel part: Use the formula for two resistors in parallel: $R_p = \frac{R_1 R_2}{R_1 + R_2}$. Substituting $3 \Omega$ and $6 \Omega$:. Calculate total series resistance: Now add the series resistor of $2 \Omega$ to the result obtained from the parallel branch:

Answer: B is correct because the parallel combination of $3 \Omega$ and $6 \Omega$ results in $2 \Omega$, which when added in series to the $2 \Omega$ resistor gives a total equivalent resistance of $4 \Omega$.

Exam Tip: Understanding series-parallel combinations is fundamental for solving complex DC networks, including bridge circuits and potential divider configurations in advanced electronics.

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