Question

In the circuit shown in figure, an ideal ohmmeter is connected across ab with the switch S open. All the connecting leads have negligible resistance. The reading of the ohmmeter will be?

Answer 1

The total resistance of the resistors connected in series is, \(R_{s}=10 \Omega+10 \Omega+10 \Omega=30 \Omega\)

The total resistance of the resistors connected in parallel is, \(\begin{aligned} R_{P} &=\frac{1}{\left(\frac{1}{20 \Omega}+\frac{1}{30 \Omega}+\frac{1}{60 \Omega}\right)} \\ &=10 \Omega \end{aligned}\)

These are connected in parallel. Therefore, the resistance across the Ohm meter is, \(\begin{aligned} R_{\text {ohm }} &=\frac{1}{\left(\frac{1}{R_{s}}+\frac{1}{R_{p}}\right)} \\ &=\frac{1}{\left(\frac{1}{30 \Omega}+\frac{1}{10 \Omega}\right)} \\ &=7.5 \Omega \end{aligned}\)