Which of the following measurements cannot be taken directly with a voltmeter?

The correct choice indicates that a voltmeter cannot be used to measure the current flowing through a circuit directly. A voltmeter is specifically designed to measure electrical potential difference, or voltage, between two points in a circuit. When you connect a voltmeter, it is inserted in parallel to the component or section of the circuit you wish to measure.

To measure current, an ammeter is required instead. An ammeter must be connected in series within the circuit so that the current flows through it. If a voltmeter were to be connected in series, it would disrupt the circuit, potentially causing a short circuit or damaging the voltmeter, as it has a high internal resistance.

In contrast, a voltmeter can successfully measure voltage across a resistor, the voltage drop in a circuit, or the voltage at a power supply, as these measurements are within its designed functionality—operating in parallel to get the correct potential difference. Thus, the ability to measure current directly with a voltmeter is not possible, which establishes the rationale behind the chosen answer.