[In these Problems neglect the internal resistance of a battery unless the Problem refers to it.]


(II) Determine the current through each resistor.

Verified step by step guidance

1. Step 1: Analyze the circuit diagram provided in the problem. Identify the arrangement of resistors (series, parallel, or a combination) and note the values of each resistor and the voltage of the battery.
2. Step 2: For resistors in series, calculate the equivalent resistance using the formula: $R_{\mathrm{eq}}=R_1+R_2+R_3$. For resistors in parallel, calculate the equivalent resistance using the formula: $R_{\mathrm{eq}}=(\frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_3})⁻1$.
3. Step 3: Once the equivalent resistance is determined, calculate the total current in the circuit using Ohm's Law: $I=\frac{V}{R_{\mathrm{eq}}}$, where $V$ is the voltage of the battery.
4. Step 4: For each resistor, determine the current flowing through it. If the resistors are in series, the current is the same through all resistors. If the resistors are in parallel, use the formula: $I=\frac{V}{R}$, where $V$ is the voltage across the resistor and $R$ is the resistance of the individual resistor.
5. Step 5: Verify your results by ensuring that the sum of currents in parallel branches equals the total current in the circuit and that the voltage drops across resistors in series add up to the total voltage of the battery.

Key Concepts

Ohm's Law

Ohm's Law states that the current (I) flowing through a conductor between two points is directly proportional to the voltage (V) across the two points and inversely proportional to the resistance (R) of the conductor. This relationship is expressed mathematically as V = IR. Understanding this law is essential for analyzing circuits and calculating the current through resistors.

Series and Parallel Circuits

In electrical circuits, resistors can be arranged in series or parallel configurations. In a series circuit, the total resistance is the sum of individual resistances, and the same current flows through each resistor. In a parallel circuit, the total resistance decreases, and the voltage across each resistor is the same, allowing for different currents to flow through each branch. Recognizing these configurations is crucial for determining the current through each resistor.

Kirchhoff's Laws

Kirchhoff's Laws consist of two principles that govern the behavior of electrical circuits. Kirchhoff's Current Law (KCL) states that the total current entering a junction equals the total current leaving it, while Kirchhoff's Voltage Law (KVL) states that the sum of the electrical potential differences around any closed circuit loop must equal zero. These laws are fundamental for analyzing complex circuits and calculating currents through individual components.