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title: "A student measures the resistance \\(R\\) of two resistors (\\(R_1 \\approx 5\\text{ }\\Omega\\) and \\(R_2 \\approx 50\\text{ k}\\Omega\\)) using a dc power supply, an ammeter with internal resistance \\(R_A \\approx 2\\text{ }\\Omega\\), and a voltmeter with internal resistance \\(R_V \\approx 100\\text{ k}\\Omega\\).  In Setup 1, the voltmeter is connected directly across the resistor while the ammeter measures the total current entering the parallel combination; this setup produces minimal percentage error for \\(R_1\\) but substantial error for \\(R_2\\).  In Setup 2, the voltmeter is connected across the series combination of the ammeter and the resistor while the ammeter measures only the resistor current; this setup produces minimal percentage error for \\(R_2\\) but substantial error for \\(R_1\\).  Which of the following statements correctly explains these experimental results?"
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url: "https://nerd-notes.com/ubq/124777/"
date_modified: "2026-09-28T14:11:14+00:00"
---

# A student measures the resistance \(R\) of two resistors (\(R_1 \approx 5\text{ }\Omega\) and \(R_2 \approx 50\text{ k}\Omega\)) using a dc power supply, an ammeter with internal resistance \(R_A \approx 2\text{ }\Omega\), and a voltmeter with internal resistance \(R_V \approx 100\text{ k}\Omega\).

In Setup 1, the voltmeter is connected directly across the resistor while the ammeter measures the total current entering the parallel combination; this setup produces minimal percentage error for \(R_1\) but substantial error for \(R_2\).

In Setup 2, the voltmeter is connected across the series combination of the ammeter and the resistor while the ammeter measures only the resistor current; this setup produces minimal percentage error for \(R_2\) but substantial error for \(R_1\).

Which of the following statements correctly explains these experimental results?

A student measures the resistance \(R\) of two resistors (\(R_1 \approx 5\text{ }\Omega\) and \(R_2 \approx 50\text{ k}\Omega\)) using a dc power supply, an ammeter with internal resistance \(R_A \approx 2\text{ }\Omega\), and a voltmeter with internal resistance \(R_V \approx 100\text{ k}\Omega\).

In Setup 1, the voltmeter is connected directly across the resistor while the ammeter measures the total current entering the parallel combination; this setup produces minimal percentage error for \(R_1\) but substantial error for \(R_2\).

In Setup 2, the voltmeter is connected across the series combination of the ammeter and the resistor while the ammeter measures only the resistor current; this setup produces minimal percentage error for \(R_2\) but substantial error for \(R_1\).

Which of the following statements correctly explains these experimental results?

![A grayscale schematic containing two circuit diagrams side-by-side, labeled Setup 1 on the left and Setup 2 on the right. Setup 1 consists of a single rectangular loop with a DC voltage source on the left wire. The top wire contains an ammeter represented by a circle with the letter A. The right side of the loop splits into two parallel branches: the inner branch contains a resistor rectangle labeled R, and the outer branch contains a voltmeter circle with the letter V. Setup 2 consists of a rectangular loop with a DC voltage source on the left wire. The right wire contains an ammeter circle with the letter A in series above a resistor rectangle labeled R. A separate parallel branch connects across both the ammeter and the resistor, containing a voltmeter circle with the letter V. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1790604674-I9BAU4.jpg)

- **A.** In Setup 1, the voltmeter acts as a high-resistance path in series with the power supply that restricts overall current for small loads, whereas in Setup 2, the ammeter low internal resistance shunts the majority of the current away from the load resistor whenever the load resistance exceeds the ammeter resistance.
- **B.** In Setup 1, the ammeter internal resistance creates an unmeasured voltage drop that dominates the calculation at high resistances, whereas in Setup 2, the voltmeter finite internal resistance creates an unmeasured current leakage that dominates the calculation at low resistances.
- **C.** In Setup 1, the small resistance dissipates significantly less thermal energy so its resistance remains constant, whereas in Setup 2, the large resistance experiences excessive Joule heating that systematically increases its resistance unless buffered in series by the ammeter.
- **D.** In Setup 1, the voltmeter draws a negligible fraction of the total measured current only when the load resistance is much smaller than \(R_V\), whereas in Setup 2, the voltage drop across the ammeter represents a negligible fraction of the total measured voltage only when the load resistance is much larger than \(R_A\).

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/124777/*