A 12 V battery is connected in series with five identical 2 k resistors. A voltmeter is connected across three of these resistors and it reads 6 V . The internal resistance of the voltmeter is:

Step-by-step solution

Let the internal resistance of the voltmeter be R_v . The circuit consists of two parts in series: the two resistors not connected to the voltmeter, and the parallel combination of the voltmeter and the three resistors. Resistance of the two series resistors: R_s = 2 2 k = 4 k Resistance of the three resistors across which the voltmeter is connected: R₃ = 3 2 k = 6 k The equivalent resistance of the parallel combination of R₃ and R_v is: R_p = 6 R_v 6 + R_v Using the voltage divider rule, the voltage across the par