Question

2.26 \times 10^{19} electrons pass through a wire in 1.31 s. what is the current in the wire?

1.63 a
2.43 a
2.01 a
2.76 a

Explanation:

Identify the given values and target variable

We are given the following values from the problem statement:

• Number of electrons, \(N = 2.26 \times 10^{19}\)
• Time interval, \(\Delta t = 1.31\text{ s}\)

We need to find the electric current, \(I\), in the wire.

Relate electric current to charge and time

Electric current is defined as the rate at which electric charge flows past a point in a circuit:

$$I = \frac{\Delta Q}{\Delta t}$$

where \(\Delta Q\) is the total charge that passes through the cross-section of the wire in time \(\Delta t\).

Calculate the total charge

The total charge \(\Delta Q\) is quantized and is equal to the number of electrons \(N\) multiplied by the elementary charge \(e\), which is the charge of a single electron:

$$e \approx 1.602 \times 10^{-19}\text{ C}$$

Using this constant, we calculate the total charge:

$$\Delta Q = N \cdot e$$

$$\Delta Q = (2.26 \times 10^{19}) \cdot (1.602 \times 10^{-19}\text{ C})$$

$$\Delta Q \approx 3.6205\text{ C}$$

Calculate the electric current

Now, we substitute the total charge \(\Delta Q\) and the time interval \(\Delta t\) into our current formula:

$$I = \frac{3.6205\text{ C}}{1.31\text{ s}}$$

$$I \approx 2.7637\text{ A}$$

Rounding to three significant figures, we get:

$$I \approx 2.76\text{ A}$$

Match with the given options

Comparing our calculated value of \(2.76\text{ A}\) with the multiple-choice options:

• \(1.63\text{ A}\)
• \(2.43\text{ A}\)
• \(2.01\text{ A}\)
• \(2.76\text{ A}\)

The correct option is \(2.76\text{ A}\).

Answer:

• (A) 1.63 A
• (B) 2.43 A
• (C) 2.01 A
• (D) 2.76 A (Correct answer)