Question

How to connect three resistors each of resistance 8 $\Omega$, so that the equivalent resistance of the combination is 12 $\Omega$? Draw diagram of the combination and justify your answer.

Hint:

Two equal resistors in parallel → Half resistance, then add series resistor.

Answer 1

Required: Equivalent resistance = 12 $\Omega$ using three 8 $\Omega$ resistors. Combination:

• Connect two 8 $\Omega$ resistors in parallel.
• Then connect this parallel combination in series with the third 8 $\Omega$ resistor.

Calculation: Step 1: Parallel combination of two resistors \[ \frac{1}{R_p} = \frac{1}{8} + \frac{1}{8} = \frac{2}{8} = \frac{1}{4} \] \[ R_p = 4 \Omega \] Step 2: Series with third resistor \[ R_{eq} = 4 + 8 = 12 \Omega \]

Diagram Description:

• Two resistors connected side by side (parallel).
• Their ends connected to a third resistor in series.

Conclusion: Two resistors in parallel and one in series give the required equivalent resistance of 12 $\Omega$.