An idealized ammeter is connected to a battery as shown in Fig. E$25.28$. Find the terminal voltage of the battery.

Verified step by step guidance

1. Identify the components in the circuit: a battery with an emf of 12.0 V, a resistor of 8.0 Ω, and another resistor of 6.0 Ω.
2. Understand that the terminal voltage of the battery is the voltage across the battery when the circuit is closed, which is the emf minus the voltage drop due to the internal resistance.
3. Calculate the total resistance in the circuit. Since the resistors are in series, the total resistance R_total is the sum of the resistances: R_total = 8.0 Ω + 6.0 Ω.
4. Use Ohm's Law to find the current I in the circuit. Ohm's Law states that I = V / R, where V is the emf of the battery and R is the total resistance.
5. Calculate the terminal voltage V_terminal using the formula V_terminal = emf - I * r, where r is the internal resistance of the battery. If the internal resistance is not given, assume it is negligible for an ideal battery.

Key Concepts

Ohm's Law

Ohm's Law states that the current through a conductor between two points is directly proportional to the voltage across the two points and inversely proportional to the resistance. It is expressed as V = IR, where V is voltage, I is current, and R is resistance. This law is fundamental for analyzing electrical circuits and calculating the current flowing through components.

Series Circuit

In a series circuit, components are connected end-to-end, forming a single path for current flow. The total resistance in a series circuit is the sum of individual resistances, and the same current flows through each component. Understanding series circuits is crucial for calculating the total resistance and voltage drops across each component, which affects the terminal voltage of the battery.

Terminal Voltage

Terminal voltage is the voltage output of a battery when it is connected in a circuit, accounting for any internal resistance. It is calculated by subtracting the voltage drop across the internal resistance from the electromotive force (EMF) of the battery. In practical terms, terminal voltage is the actual voltage available to the external circuit, which can be less than the battery's EMF due to internal resistance.