A current of `2 A`, passing through a conductor produces `80 J` of heat in `10 s`. The resistance of the conductor in ohm is:
(1.) 0.5
(2.) 2
(3.) 4
(4.) 20

Options

A. `0.5`
B. `2`
C. `4`
D. `20`

Answer

To find the resistance of the conductor, we can use the formula for heat produced in a conductor due to current, which is given by:

\[ H = I^2 R t \]

Where:
- \( H \) = heat produced (in joules)
- \( I \) = current (in amperes)
- \( R \) = resistance (in ohms)
- \( t \) = time (in seconds)

Given:
- \( H = 80 \, \text{J} \)
- \( I = 2 \, \text{A} \)
- \( t = 10 \, \text{s} \)

### Step 1: Rearranging the formula
We want to find the resistance \( R \). Rearranging the formula gives us:

\[ R = \frac{H}{I^2 t} \]

### Step 2: Substituting the values
Now we can substitute the known values into the equation:

\[ R = \frac{80 \, \text{J}}{(2 \, \text{A})^2 \times 10 \, \text{s}} \]

### Step 3: Calculating \( I^2 \)
Calculating \( I^2 \):

\[ I^2 = (2 \, \text{A})^2 = 4 \, \text{A}^2 \]

### Step 4: Substituting \( I^2 \) back into the equation
Now substituting \( I^2 \) back into the equation for \( R \):

\[ R = \frac{80 \, \text{J}}{4 \, \text{A}^2 \times 10 \, \text{s}} \]

### Step 5: Calculating the denominator
Calculating the denominator:

\[ 4 \, \text{A}^2 \times 10 \, \text{s} = 40 \, \text{A}^2 \cdot \text{s} \]

### Step 6: Final calculation of \( R \)
Now, substituting this value back into the equation for \( R \):

\[ R = \frac{80 \, \text{J}}{40 \, \text{A}^2 \cdot \text{s}} = 2 \, \Omega \]

### Conclusion
The resistance of the conductor is \( R = 2 \, \Omega \).

The correct option is (2) 2.

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