A potential difference of 10 V is applied across a conductor of resistance `1 k Omega`. Find the number of electrons flowing through the conductor in 5 minutes.

Options

A. `1.875 xx 10^(16)`
B. `1.875 xx 10^(17)`
C. `1.875 xx 10^(22)`
D. `1.875 xx 10^(19)`

Answer

To solve the problem step by step, we will follow the outlined approach based on the provided information.

### Given Data:
1. Potential difference (V) = 10 V
2. Resistance (R) = 1 kΩ = 1000 Ω
3. Time (t) = 5 minutes = 5 × 60 seconds = 300 seconds

### Step 1: Calculate the Current (I)
Using Ohm's Law, the current (I) can be calculated using the formula:
\[ I = \frac{V}{R} \]

Substituting the values:
\[ I = \frac{10 \, \text{V}}{1000 \, \Omega} = 0.01 \, \text{A} \]

### Step 2: Calculate the Total Charge (Q)
The total charge (Q) that flows through the conductor can be calculated using the formula:
\[ Q = I \times t \]

Substituting the values:
\[ Q = 0.01 \, \text{A} \times 300 \, \text{s} = 3 \, \text{C} \]

### Step 3: Calculate the Number of Electrons (n)
The total charge (Q) can also be expressed in terms of the number of electrons (n) using the formula:
\[ Q = n \times e \]
where \( e \) (the charge of one electron) is approximately \( 1.6 \times 10^{-19} \, \text{C} \).

Rearranging the formula to find n:
\[ n = \frac{Q}{e} \]

Substituting the values:
\[ n = \frac{3 \, \text{C}}{1.6 \times 10^{-19} \, \text{C/electron}} \]

Calculating n:
\[ n = \frac{3}{1.6 \times 10^{-19}} \approx 1.875 \times 10^{19} \]

### Final Answer:
The number of electrons flowing through the conductor in 5 minutes is approximately:
\[ n \approx 1.875 \times 10^{19} \]

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