A resistor whose value \( R = 10 \Omega \) is connected to a 10-volt battery. What will be the power \( P \) and the amount of heat \( H \) generated in one minute?
\( P = 10 \) W, \( H = 600 \) J
To solve this problem, we need to determine the power \( P \) consumed by a resistor and the heat \( H \) generated in one minute.
The given values are:
- Voltage \( V = 10 \) volts
- Resistance \( R = 10 \Omega \)
Step 1: Calculate the Power \( P \)
The formula for power \( P \) using Ohm’s Law is:
\[ P = \frac{V^2}{R} \]
Substituting the given values:
\[ P = \frac{10^2}{10} = \frac{100}{10} = 10 \text{ W} \]
Step 2: Calculate the Heat \( H \) Generated in One Minute
Heat generated \( H \) is given by:
\[ H = P \times t \]
Where time \( t = 60 \) seconds (since 1 minute = 60 seconds).
Substituting the values:
\[ H = 10 \times 60 = 600 \text{ J} \]
Conclusion: The power and heat generated are \( P = 10 \) W and \( H = 600 \) J, respectively.
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