A 4.5-V battery is connected to a bulb whose resistance is 2.3 Ω. How many electrons leave the battery per minute?

Verified step by step guidance

1. Step 1: Use Ohm's Law to calculate the current (I) flowing through the circuit. Ohm's Law is given by $I=\frac{V}{R}$, where $V$ is the voltage (4.5 V) and $R$ is the resistance (2.3 Ω).
2. Step 2: Once the current $I$ is determined, calculate the total charge (Q) that flows through the circuit in one minute. Use the formula $Q=It$, where $t$ is the time in seconds (1 minute = 60 seconds).
3. Step 3: Recall that the charge of a single electron is approximately $e_{-}=1.6\times {10}^{-}C$. To find the number of electrons, divide the total charge $Q$ by the charge of a single electron using the formula $n=\frac{Q}{e_{-}}$.
4. Step 4: Substitute the values for $Q$ (from Step 2) and $e_{-}$ into the formula to calculate the number of electrons $n$.
5. Step 5: Ensure the units are consistent throughout the calculation and verify the result to confirm it makes physical sense (e.g., the number of electrons should be a very large number).

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. It is mathematically expressed as V = I × R. This relationship is crucial for determining the current in the circuit when a voltage is applied to a resistor.

Current and Charge

Electric current is the flow of electric charge, typically measured in amperes (A). One ampere is defined as one coulomb of charge passing through a point in a circuit per second. Understanding the relationship between current and charge is essential for calculating how many electrons flow through the circuit over a given time period.

Elementary Charge

The elementary charge is the smallest unit of electric charge, represented by the symbol 'e', and is approximately equal to 1.6 × 10^-19 coulombs. Since electrons carry a negative charge equal to this value, knowing the charge of an electron is necessary to convert the total charge flowing in the circuit into the number of electrons that pass through.