Sure, let's solve these problems step-by-step.
### Problem 1
Question: What voltage difference is needed to change the potential energy of a 0.005-C charge by 1.5 J?
Solution:
1. The relationship between voltage (V), charge (Q), and energy (E) can be expressed by the formula:
[tex]\[
V = \frac{E}{Q}
\][/tex]
where
- [tex]\( E \)[/tex] is the change in potential energy,
- [tex]\( Q \)[/tex] is the charge, and
- [tex]\( V \)[/tex] is the voltage difference.
2. We are given:
- [tex]\( E = 1.5 \)[/tex] Joules,
- [tex]\( Q = 0.005 \)[/tex] Coulombs.
3. Substitute the given values into the formula:
[tex]\[
V = \frac{1.5 \, \text{J}}{0.005 \, \text{C}}
\][/tex]
4. Perform the division:
[tex]\[
V = \frac{1.5}{0.005} = 300 \, \text{Volts}
\][/tex]
Answer: The voltage difference needed is 300 Volts.
### Problem 2
Question: How much energy does an object with a charge of 0.002 C gain if it passes through a voltage of 15 V?
Solution:
1. The relationship between energy (E), charge (Q), and voltage (V) can be expressed by the formula:
[tex]\[
E = Q \cdot V
\][/tex]
where
- [tex]\( E \)[/tex] is the energy gained,
- [tex]\( Q \)[/tex] is the charge, and
- [tex]\( V \)[/tex] is the voltage.
2. We are given:
- [tex]\( Q = 0.002 \)[/tex] Coulombs,
- [tex]\( V = 15 \)[/tex] Volts.
3. Substitute the given values into the formula:
[tex]\[
E = 0.002 \, \text{C} \cdot 15 \, \text{V}
\][/tex]
4. Perform the multiplication:
[tex]\[
E = 0.002 \times 15 = 0.03 \, \text{Joules}
\][/tex]
Answer: The energy gained is 0.03 Joules.
By following these steps, you should have a clear understanding of how to solve similar problems involving the relationships between voltage, charge, and energy.
