Which of the four circuits actually measures the voltage across R?

A voltmeter must have its two terminals connected to the two terminals of the resistor R to measure the voltage across R. **Answer:** only circuits **1** and **3** are correct. **Why:** - A voltmeter measures the potential difference between the two nodes to which its terminals are attached. To read the voltage across R it must be connected to the two nodes that are the endpoints of R (i.e. in parallel with R). - In circuits 1 and 3 the meter’s two leads are attached to the two endpoints of R, so the instrument reads the voltage drop across R (even though the meter’s finite internal resistance Rₚ draws some extra current and thus slightly changes the circuit). - In circuits 2 and 4 at least one voltmeter lead is not on one of R’s endpoints (the meter is effectively connected to different nodes or into the supply loop), so the meter does not show the voltage across R but some other potential difference. So only **(1) and (3)** measure the voltage across R correctly (i.e. the voltmeter is connected across the resistor’s two terminals).