Question

A 12-V battery is connected across a 100-Ω resistor. How many electrons flow through the wire in 5.0 min?

Answer 1

To calculate the number of electrons flowing through the wire:

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Step 1: Calculate the current using Ohm's Law

$$I = \frac{V}{R}$$

Where:

• $V = 12 \, \text{V}$

• $R = 100 \, \Omega$

$$I = \frac{12}{100} = 0.12 \, \text{A}$$

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Step 2: Calculate the total charge that flows in 5.0 minutes

Time:

$$t = 5.0 \times 60 = 300 \, \text{seconds}$$

Charge:

$$Q = I \times t = 0.12 \times 300 = 36.0 \, \text{C}$$

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Step 3: Calculate the number of electrons

Each electron has a charge of:

$$e = 1.602 \times 10^{-19} \, \text{C}$$$$\text{Number of electrons} = \frac{Q}{e} = \frac{36.0}{1.602 \times 10^{-19}} \approx 2.25 \times 10^{20} \, \text{electrons}$$

Final answer: Approximately $2.25 \times 10^{20}$ electrons.

4o

Answer 2