Let's analyze each sentence one by one using Ohm's law, which is [tex]\( I = \frac{V}{R} \)[/tex]:
1. If the current increases, then the resistance increases. Assume voltage is constant.
- According to Ohm's law, with voltage (V) being constant, an increase in current (I) would require the resistance (R) to decrease. Therefore, this statement is false.
2. If the resistance decreases, then the current increases. Assume voltage is constant.
- With voltage (V) constant, a decrease in resistance (R) would cause the current (I) to increase. This is consistent with Ohm's law. Therefore, this statement is true.
3. If the voltage increases, then the resistance decreases. Assume current is constant.
- For current (I) to be constant, if voltage (V) increases, resistance (R) must also increase. Therefore, this statement is false.
4. If the voltage increases, then the current increases. Assume resistance is constant.
- With resistance (R) being constant, an increase in voltage (V) would result in an increase in current (I). Therefore, this statement is true.
5. If the voltage increases, then the current decreases. Assume resistance is constant.
- This is the opposite of the previous statement. If resistance (R) is constant and voltage (V) increases, current (I) would also increase, not decrease. Therefore, this statement is false.
So, the correct answers are:
- If the resistance decreases, then the current increases. Assume voltage is constant.
- If the voltage increases, then the current increases. Assume resistance is constant.
