A 10 V storage battery of negligible internal resistance is connected across a `50Omega` resistor. How much heat energy is produced in the resistor in 1 hour

Options

A. 7200J
B. 6200J
C. 5200J
D. 4200J

Answer

To solve the problem of how much heat energy is produced in a 50Ω resistor connected to a 10V battery over the course of one hour, we can follow these steps:

### Step 1: Identify the given values
- Voltage (V) = 10 V
- Resistance (R) = 50 Ω
- Time (t) = 1 hour

### Step 2: Convert time from hours to seconds
Since we need to calculate energy in Joules, we should convert the time into seconds:
\[ t = 1 \text{ hour} = 60 \text{ minutes} \times 60 \text{ seconds/minute} = 3600 \text{ seconds} \]

### Step 3: Use the formula for heat energy produced
The heat energy (H) produced in a resistor can be calculated using the formula:
\[ H = \frac{V^2 \cdot t}{R} \]
where:
- \(H\) is the heat energy in Joules,
- \(V\) is the voltage in volts,
- \(t\) is the time in seconds,
- \(R\) is the resistance in ohms.

### Step 4: Substitute the values into the formula
Now, substituting the known values into the formula:
\[ H = \frac{(10 \text{ V})^2 \cdot (3600 \text{ s})}{50 \text{ Ω}} \]

### Step 5: Calculate \(H\)
Calculating the square of the voltage:
\[ (10 \text{ V})^2 = 100 \text{ V}^2 \]
Now substituting this back into the equation:
\[ H = \frac{100 \cdot 3600}{50} \]
Calculating the numerator:
\[ 100 \cdot 3600 = 360000 \]
Now divide by the resistance:
\[ H = \frac{360000}{50} = 7200 \text{ J} \]

### Step 6: Conclusion
The heat energy produced in the resistor in one hour is:
\[ H = 7200 \text{ Joules} \]

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