Problem Analysis:
We need to calculate the heat generated when a specific amount of charge moves across a given potential difference. The key quantities provided are:
- Charge (\(Q\)): 96000 Coulombs (C)
- Potential Difference (\(V\)): 50 Volts (V)
- Time (\(t\)): 1 hour (This information is context, but not directly needed for the calculation using the formula \(H = Q \times V\)).
Calculating Heat Generated
The heat generated (which is equivalent to the electrical energy transferred) when a charge \(Q\) moves through a potential difference \(V\) is given by the formula:
\(H = Q \times V\)
Where:
- \(H\) is the Heat generated (in Joules, J)
- \(Q\) is the Charge transferred (in Coulombs, C)
- \(V\) is the Potential Difference (in Volts, V)
Step-by-Step Calculation
-
Substitute the given values into the formula:
\(H = 96000 \text{ C} \times 50 \text{ V}\)
-
Perform the multiplication:
\(H = 4,800,000 \text{ J}\)
-
Express the answer in scientific notation:
To match the format of the options, we convert 4,800,000 J to scientific notation:
\(H = 4.8 \times 10^6 \text{ J}\)
Final Answer Derivation
The calculated heat generated is \(4.8 \times 10^6\) J. This matches one of the provided options.
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