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


(II) Determine the voltage across each resistor

Verified step by step guidance

1. Step 1: Analyze the circuit diagram provided in the problem. Identify the configuration of the resistors (series, parallel, or a combination) and note the values of the resistances and the total voltage supplied by the battery.
2. Step 2: Use Ohm's Law, which states \( V = IR \), to relate the voltage \( V \), current \( I \), and resistance \( R \). Determine the equivalent resistance of the circuit if the resistors are in series or parallel.
3. Step 3: Calculate the total current in the circuit using the formula \( I = \frac{V_{total}}{R_{eq}} \), where \( V_{total} \) is the total voltage supplied by the battery and \( R_{eq} \) is the equivalent resistance of the circuit.
4. Step 4: For each resistor, calculate the voltage across it using \( V = IR \). If the resistors are in series, the current through each resistor is the same, and you can directly multiply the current by the resistance of each resistor. If the resistors are in parallel, the voltage across each resistor is the same, and you can use \( I = \frac{V}{R} \) to find the current through each resistor.
5. Step 5: Verify your results by ensuring that the sum of the voltages across all resistors in series equals the total voltage supplied by the battery, or that the currents in all branches of a parallel circuit add up to the total current supplied by 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 determining the voltage across each resistor.

Series and Parallel Circuits

In electrical circuits, resistors can be arranged in series or parallel configurations. In a series circuit, the same current flows through each resistor, and the total voltage is the sum of the voltages across each resistor. In a parallel circuit, the voltage across each resistor is the same, and the total current is the sum of the currents through each resistor. Recognizing these configurations is crucial for calculating voltages in the given problem.

Voltage Division

Voltage division is a technique used to determine the voltage drop across each resistor in a series circuit. According to this principle, the voltage across a resistor in series is proportional to its resistance relative to the total resistance of the circuit. This concept is vital for solving problems that require finding the voltage across individual resistors when connected in series.