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:
\(\[
V = \frac{E}{Q}
\]\)
where
- \(\( E \)\) is the change in potential energy,
- \(\( Q \)\) is the charge, and
- \(\( V \)\) is the voltage difference.
2. We are given:
- \(\( E = 1.5 \)\) Joules,
- \(\( Q = 0.005 \)\) Coulombs.
3. Substitute the given values into the formula:
\(\[
V = \frac{1.5 \, \text{J}}{0.005 \, \text{C}}
\]\)
4. Perform the division:
\(\[
V = \frac{1.5}{0.005} = 300 \, \text{Volts}
\]\)
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:
\(\[
E = Q \cdot V
\]\)
where
- \(\( E \)\) is the energy gained,
- \(\( Q \)\) is the charge, and
- \(\( V \)\) is the voltage.
2. We are given:
- \(\( Q = 0.002 \)\) Coulombs,
- \(\( V = 15 \)\) Volts.
3. Substitute the given values into the formula:
\(\[
E = 0.002 \, \text{C} \cdot 15 \, \text{V}
\]\)
4. Perform the multiplication:
\(\[
E = 0.002 \times 15 = 0.03 \, \text{Joules}
\]\)
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.
