A boy records that 4000 Joule of work is required to transfer 10 coulomb of charge between two points of a resistor of 50n. The current passing through It is

Options

A. `2 A`
B. `4 A`
C. `8 A`
D. `16 A`

Explanation

To find the current passing through the resistor, we can follow these steps:

### Step 1: Understand the relationship between work, voltage, and charge
The work done (W) in transferring a charge (Q) across a potential difference (V) is given by the formula:
\[ W = V \times Q \]

### Step 2: Substitute the known values into the equation
From the problem, we know:
- Work done, \( W = 4000 \, \text{Joules} \)
- Charge transferred, \( Q = 10 \, \text{Coulombs} \)

We can rearrange the formula to solve for voltage (V):
\[ V = \frac{W}{Q} \]

### Step 3: Calculate the voltage
Substituting the known values into the equation:
\[ V = \frac{4000 \, \text{J}}{10 \, \text{C}} = 400 \, \text{Volts} \]

### Step 4: Use Ohm's law to find the current
Ohm's law states that:
\[ V = I \times R \]
where \( I \) is the current and \( R \) is the resistance.

Given that the resistance \( R = 50 \, \text{Ohms} \), we can rearrange the equation to solve for current (I):
\[ I = \frac{V}{R} \]

### Step 5: Substitute the values to find the current
Now substituting the values of voltage and resistance:
\[ I = \frac{400 \, \text{Volts}}{50 \, \text{Ohms}} = 8 \, \text{Amperes} \]

### Conclusion
The current passing through the resistor is:
\[ I = 8 \, \text{A} \]

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