The energy required to charge a 10 μF capacitor to 100 V is
0.05 J
Calculating Capacitor Energy: 10 μF to 100 V
This problem asks us to find the energy stored in a capacitor when it is charged to a specific voltage. We are given the capacitance (C) and the final voltage (V).
Capacitor Energy Formula
The energy stored in a capacitor is the amount of work done to charge it. The standard formula to calculate this energy (U) is:
\( U = \frac{1}{2} C V^2 \)
Where:
\( U \)is the energy stored, measured in Joules (J).\( C \)is the capacitance, measured in Farads (F).\( V \)is the voltage across the capacitor, measured in Volts (V).
Step-by-Step Calculation
Let's calculate the energy using the given values:
- Identify Given Values:
- Capacitance,
\( C = 10 \, \mu\text{F} \) - Voltage,
\( V = 100 \, \text{V} \)
- Capacitance,
- Convert Units: The capacitance is given in microfarads ($\mu$F), which needs to be converted to Farads (F) for the calculation.
\( 1 \, \mu\text{F} = 1 \times 10^{-6} \, \text{F} \)- So,
\( C = 10 \times 10^{-6} \, \text{F} \)
- Apply the Formula: Substitute the values into the energy formula.
\( U = \frac{1}{2} C V^2 \)\( U = \frac{1}{2} \times (10 \times 10^{-6} \, \text{F}) \times (100 \, \text{V})^2 \)
- Perform the Calculation:
- First, calculate
\( V^2 \):\( (100 \, \text{V})^2 = 10000 \, \text{V}^2 \) - Now substitute this back:
\( U = \frac{1}{2} \times (10 \times 10^{-6}) \times 10000 \) \( U = 5 \times 10^{-6} \times 10000 \)\( U = 5 \times 10^{-6} \times 10^4 \)\( U = 5 \times 10^{-6 + 4} \)\( U = 5 \times 10^{-2} \, \text{J} \)
- First, calculate
- Final Result: Convert the scientific notation to a decimal.
\( U = 0.05 \, \text{J} \)
Conclusion
The energy required to charge a 10 μF capacitor to 100 V is 0.05 Joules. This matches the second option provided.
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