For a current set up in wire for 28.0 d, a total of `1.36 xx 10^(26)` electrons pass through any cross section across the wire's width at a steady rate. What is the current?

Answer

To find the current flowing through the wire, we can use the formula for current (I):

\[ I = \frac{Q}{T} \]

Where:
- \( Q \) is the total charge that passes through a cross-section of the wire,
- \( T \) is the time in seconds.

### Step 1: Calculate the total charge (Q)

The total charge \( Q \) can be calculated using the number of electrons (\( N \)) and the charge of a single electron (\( e \)):

\[ Q = N \times e \]

Given:
- \( N = 1.36 \times 10^{26} \) electrons
- Charge of an electron \( e = 1.6 \times 10^{-19} \) coulombs

Substituting the values:

\[ Q = 1.36 \times 10^{26} \times 1.6 \times 10^{-19} \]

### Step 2: Calculate Q

Now, we perform the multiplication:

\[ Q = 1.36 \times 1.6 \times 10^{26 - 19} \]
\[ Q = 2.176 \times 10^{7} \text{ coulombs} \]

### Step 3: Calculate the time (T)

The time \( T \) is given as 28 days. We need to convert this into seconds:

\[ T = 28 \text{ days} \times 24 \text{ hours/day} \times 3600 \text{ seconds/hour} \]

Calculating \( T \):

\[ T = 28 \times 24 \times 3600 \]
\[ T = 28 \times 86400 \]
\[ T = 2419200 \text{ seconds} \]

### Step 4: Calculate the current (I)

Now we can substitute \( Q \) and \( T \) into the current formula:

\[ I = \frac{Q}{T} = \frac{2.176 \times 10^{7}}{2419200} \]

### Step 5: Perform the division

Calculating \( I \):

\[ I \approx 9.0 \text{ amperes} \]

### Final Answer

The current flowing through the wire is approximately **9.0 A**.

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