Questions: In the circuit shown in the 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 closest to

Solution Steps

When the switch S is open, the right part of the circuit containing the 10 Ω resistor and the battery is disconnected. Thus, the ohmmeter only sees the left part of the circuit.

Between points a and b, we have three resistors: 20 Ω, 30 Ω, and 60 Ω. The 30 Ω resistor is in series with the 60 Ω resistor. Their equivalent resistance is \(30 + 60 = 90\) Ω. This 90 Ω equivalent resistance is in parallel with the 20 Ω resistor.

Let the equivalent resistance between a and b be \(R_{ab}\). The formula for parallel resistors is given by: \( \frac{1}{R_{ab}} = \frac{1}{20} + \frac{1}{90} \) \( \frac{1}{R_{ab}} = \frac{90 + 20}{20 \times 90} = \frac{110}{1800} = \frac{11}{180} \) \( R_{ab} = \frac{180}{11} \approx 16.36 \) Ω.

Final Answer