To find the values of \( w \) (energy stored in the capacitor) and \( q \) (charge on the capacitor), you can use the following formulas related to capacitors.
Charge \( q \) on a capacitor is given by the formula: \[ q = C \cdot U \] where:
- \( C \) is the capacitance in farads (F)
- \( U \) is the voltage in volts (V)
Energy \( w \) stored in a capacitor is given by the formula: \[ w = \frac{1}{2} C U^2 \]
Now, substituting your values:
Given:
- \( C = 1 \, \mu\text{F} = 1 \times 10^{-6} \, \text{F} \)
- \( U = 10 \, \text{V} \)
Calculate \( q \): \[ q = (1 \times 10^{-6} \, \text{F}) \cdot (10 \, \text{V}) = 1 \times 10^{-5} \, \text{C} = 10 \, \mu\text{C} \]
Calculate \( w \): \[ w = \frac{1}{2} (1 \times 10^{-6} \, \text{F}) (10 \, \text{V})^2 \] \[ w = \frac{1}{2} (1 \times 10^{-6} \, \text{F}) (100 \, \text{V}^2) = \frac{1}{2} \times 1 \times 10^{-4} \, \text{J} = 0.5 \times 10^{-4} \, \text{J} = 5 \times 10^{-5} \, \text{J} = 50 \, \text{μJ} \]
In summary:
- \( q = 10 \, \mu\text{C} \)
- \( w = 50 \, \mu\text{J} \)