To determine the energy stored in a capacitor given its charge and the voltage applied, we can use the formula for the energy (E) stored in a capacitor:
[tex]\[ E = \frac{1}{2} Q V \][/tex]
where:
- [tex]\( E \)[/tex] is the energy stored,
- [tex]\( Q \)[/tex] is the charge stored in the capacitor,
- [tex]\( V \)[/tex] is the voltage applied across the capacitor.
In this problem, we are given:
- Charge, [tex]\( Q = 4.33 \times 10^{-7} \)[/tex] Coulombs,
- Voltage, [tex]\( V = 3.45 \)[/tex] Volts.
### Step-by-Step Solution
1. Substitute the given values into the energy formula:
[tex]\[ E = \frac{1}{2} \times 4.33 \times 10^{-7} \, \text{C} \times 3.45 \, \text{V} \][/tex]
2. Compute the product inside the formula:
First, multiply the charge by the voltage:
[tex]\[ 4.33 \times 10^{-7} \, \text{C} \times 3.45 \, \text{V} = 14.9385 \times 10^{-7} \][/tex]
Now, multiply by [tex]\( \frac{1}{2} \)[/tex]:
[tex]\[ \frac{1}{2} \times 14.9385 \times 10^{-7} = 7.46925 \times 10^{-7} \, \text{J} \][/tex]
3. Express the energy in the desired scientific notation format:
The energy can be expressed in scientific notation:
[tex]\[ 7.46925 \times 10^{-7} \][/tex]
### Final Answer
Therefore, the energy stored in the capacitor is:
[tex]\[
\boxed{7.46925 \times 10^{-7} \text{ J}}
\][/tex]
The coefficient is [tex]\( 7.46925 \)[/tex] (green), and the exponent is [tex]\( -7 \)[/tex] (yellow).
