Question

Three resistances of values 2$\Omega$, 3$\Omega$ and 6$\Omega$ are to be connected to produce an effective resistance of 4$\Omega$ . This can be done by connecting

• A. 6$\Omega$ resistance in series with the parallel combination of 2$\Omega$ and 3$\Omega$
• B. 3$\Omega$resistance in series with the parallel combination of 2$\Omega$ and 6$\Omega$
• C. 2$\Omega$resistance in series with the parallel combination of 3$\Omega$ and 6$\Omega$
• D. 2$\Omega$ resistance in parallel with the parallel combination of 3$\Omega$ and 6$\Omega$

Answer 1

The Correct Option is C

In a parallel combination of resistors, the equivalent resistance is given by:

\(R_p = \frac{R_1 R_2}{R_1 + R_2}\)

For \(3\,\Omega\) and \(6\,\Omega\):

\(R_p = \frac{3 \times 6}{3 + 6} = \frac{18}{9} = 2\,\Omega\)

Now this equivalent resistance is in series with \(2\,\Omega\), so total resistance is:

\(R_{\text{eq}} = 2 + 2 = 4\,\Omega\)

Final equivalent resistance = \(4\,\Omega\)