An idealized ammeter is connected to a battery as shown in Fig. E$25.28$. Find the current through the $4.00$-$\Omega$ resistor.

Verified step by step guidance

1. Identify the components in the circuit: a 9.0 V battery, a 6.0 Ω resistor, a 10.0 Ω resistor, and an ideal ammeter. The ammeter is connected in parallel with the 10.0 Ω resistor.
2. Apply Ohm's Law, which states that V = I * R, to find the total current in the circuit. First, calculate the equivalent resistance of the circuit. Since the ammeter is ideal, it does not affect the circuit's resistance.
3. Calculate the equivalent resistance of the circuit. The 6.0 Ω resistor is in series with the parallel combination of the 10.0 Ω resistor and the ammeter. The equivalent resistance of the parallel section is the same as the 10.0 Ω resistor because the ammeter is ideal.
4. Add the resistance of the 6.0 Ω resistor to the equivalent resistance of the parallel section to find the total resistance in the circuit: R_total = 6.0 Ω + 10.0 Ω.
5. Use Ohm's Law to find the total current supplied by the battery: I_total = V / R_total, where V is the battery voltage (9.0 V) and R_total is the total resistance calculated in the previous step.

Key Concepts

Ohm's Law

Ohm's Law is a fundamental principle in electronics and physics that relates voltage (V), current (I), and resistance (R) in an electrical circuit. It is expressed by the equation V = IR, indicating that the voltage across a resistor is the product of the current flowing through it and its resistance. This law is essential for calculating the current in the circuit when the voltage and resistance are known.

Series and Parallel Circuits

In a series circuit, components are connected end-to-end, so the same current flows through each component. In a parallel circuit, components are connected across the same voltage source, allowing the current to divide among the paths. Understanding these configurations is crucial for analyzing the circuit in the image, as it helps determine how the total resistance and current are distributed.

Kirchhoff's Voltage Law

Kirchhoff's Voltage Law states that the sum of the electrical potential differences (voltage) around any closed network is zero. This principle is used to analyze complex circuits by ensuring that the total voltage supplied by the battery is equal to the sum of the voltage drops across each component in the loop. It is vital for solving the circuit problem presented in the image.