An electric current of `2.0` A passes through a wire of resistance `25 Omega`. How much heat will be developed in 1 minute?

Explanation

To solve the problem of how much heat will be developed in a wire when an electric current passes through it, we can use Joule's law of heating. Here's a step-by-step solution:

### Step 1: Identify the given values
- Current (I) = 2.0 A
- Resistance (R) = 25 Ω
- Time (t) = 1 minute = 60 seconds

### Step 2: Write the formula for heat produced
According to Joule's law, the heat (H) produced in a resistor is given by the formula:
\[ H = I^2 \times R \times t \]
where:
- \( H \) is the heat energy in Joules,
- \( I \) is the current in Amperes,
- \( R \) is the resistance in Ohms,
- \( t \) is the time in seconds.

### Step 3: Substitute the values into the formula
Now, substitute the values into the formula:
\[ H = (2.0 \, \text{A})^2 \times (25 \, \Omega) \times (60 \, \text{s}) \]

### Step 4: Calculate \( I^2 \)
Calculate \( I^2 \):
\[ (2.0 \, \text{A})^2 = 4.0 \, \text{A}^2 \]

### Step 5: Substitute \( I^2 \) back into the equation
Now substitute \( I^2 \) back into the equation:
\[ H = 4.0 \, \text{A}^2 \times 25 \, \Omega \times 60 \, \text{s} \]

### Step 6: Multiply the values
Now, calculate the product:
\[ H = 4.0 \times 25 \times 60 \]
First, calculate \( 4.0 \times 25 \):
\[ 4.0 \times 25 = 100 \]
Then multiply by 60:
\[ 100 \times 60 = 6000 \]

### Step 7: State the final answer
Thus, the heat developed in the wire in 1 minute is:
\[ H = 6000 \, \text{Joules} \]

### Summary
The heat developed in the wire when a current of 2.0 A passes through a resistance of 25 Ω for 1 minute is **6000 Joules**.

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