In the circuit shown in Fig. E26.33 all meters are idealized and the batteries have no appreciable internal resistance.
(a) Find the reading of the voltmeter with the switch S open. Which point is at a higher potential: a or b?

Verified step by step guidance

1. Identify the components in the circuit: two batteries (10.00V and 30.00V), three resistors (25.00Ω, 50.00Ω, and 5.00Ω), a voltmeter V1, and a switch S.
2. Since the switch S is open, no current flows through the 5.00Ω resistor. Therefore, the circuit can be simplified by ignoring the branch containing the 5.00Ω resistor and the switch S.
3. Calculate the potential difference across the 50.00Ω resistor. Since no current flows through it (open switch), the potential difference across it is zero.
4. Determine the potential at point M. The potential at point M is the same as the potential of the 30.00V battery because there is no voltage drop across the 50.00Ω resistor.
5. Calculate the reading of the voltmeter V1. The voltmeter measures the potential difference between points a and b. Since point a is connected to the 10.00V battery and point b is connected to the 30.00V battery, the reading of the voltmeter V1 is the difference between these two potentials.

Key Concepts

Kirchhoff's Loop Rule

Kirchhoff's Loop Rule states that the sum of the potential differences (voltage) around any closed loop in a circuit must equal zero. This principle is essential for analyzing circuits, as it allows us to account for all voltage gains and drops, ensuring that energy is conserved within the loop.

Voltage Measurement

Voltage is the electric potential difference between two points in a circuit. When measuring voltage with a voltmeter, it is important to connect the voltmeter across the two points of interest. The reading indicates how much energy per unit charge is available to move charges between those points, which is crucial for understanding circuit behavior.

Ideal Meters

Ideal meters, such as ideal voltmeters and ammeters, are theoretical devices that do not affect the circuit they are measuring. An ideal voltmeter has infinite resistance, meaning it draws no current, while an ideal ammeter has zero resistance, allowing it to measure current without altering the circuit. This concept simplifies circuit analysis by allowing us to treat these meters as non-influential components.