Answer :
Certainly! Let's analyze each statement step-by-step according to Ohm's Law, which is stated as [tex]\( I = \frac{V}{R} \)[/tex]:
1. If the current increases, then the resistance increases. Assume voltage is constant.
According to Ohm's Law:
[tex]\[ I = \frac{V}{R} \][/tex]
If the voltage [tex]\( V \)[/tex] is constant and the current [tex]\( I \)[/tex] increases, then in order to balance the equation, the resistance [tex]\( R \)[/tex] must decrease. Therefore, this statement is False.
2. If the resistance decreases, then the current increases. Assume voltage is constant.
Again, according to Ohm's Law:
[tex]\[ I = \frac{V}{R} \][/tex]
If the voltage [tex]\( V \)[/tex] is constant and the resistance [tex]\( R \)[/tex] decreases, then the current [tex]\( I \)[/tex] must increase. Therefore, this statement is True.
3. If the voltage increases, then the resistance decreases. Assume current is constant.
According to Ohm's Law:
[tex]\[ I = \frac{V}{R} \][/tex]
If the current [tex]\( I \)[/tex] is constant and the voltage [tex]\( V \)[/tex] increases, then the resistance [tex]\( R \)[/tex] must also increase to keep the current [tex]\( I \)[/tex] constant. Therefore, this statement is False.
4. If the voltage increases, then the current increases. Assume resistance is constant.
According to Ohm's Law:
[tex]\[ I = \frac{V}{R} \][/tex]
If the resistance [tex]\( R \)[/tex] is constant and the voltage [tex]\( V \)[/tex] increases, then the current [tex]\( I \)[/tex] must increase. Therefore, this statement is True.
5. If the voltage increases, then the current decreases. Assume resistance is constant.
Using Ohm’s Law:
[tex]\[ I = \frac{V}{R} \][/tex]
If the resistance [tex]\( R \)[/tex] is constant and the voltage [tex]\( V \)[/tex] increases, then the current [tex]\( I \)[/tex] must also increase, not decrease. Therefore, this statement is False.
Thus, the two true statements are:
- Statement 2: If the resistance decreases, then the current increases. Assume voltage is constant.
- Statement 4: If the voltage increases, then the current increases. Assume resistance is constant.
The true statements are:
[tex]\[ \boxed{[2, 4]} \][/tex]
1. If the current increases, then the resistance increases. Assume voltage is constant.
According to Ohm's Law:
[tex]\[ I = \frac{V}{R} \][/tex]
If the voltage [tex]\( V \)[/tex] is constant and the current [tex]\( I \)[/tex] increases, then in order to balance the equation, the resistance [tex]\( R \)[/tex] must decrease. Therefore, this statement is False.
2. If the resistance decreases, then the current increases. Assume voltage is constant.
Again, according to Ohm's Law:
[tex]\[ I = \frac{V}{R} \][/tex]
If the voltage [tex]\( V \)[/tex] is constant and the resistance [tex]\( R \)[/tex] decreases, then the current [tex]\( I \)[/tex] must increase. Therefore, this statement is True.
3. If the voltage increases, then the resistance decreases. Assume current is constant.
According to Ohm's Law:
[tex]\[ I = \frac{V}{R} \][/tex]
If the current [tex]\( I \)[/tex] is constant and the voltage [tex]\( V \)[/tex] increases, then the resistance [tex]\( R \)[/tex] must also increase to keep the current [tex]\( I \)[/tex] constant. Therefore, this statement is False.
4. If the voltage increases, then the current increases. Assume resistance is constant.
According to Ohm's Law:
[tex]\[ I = \frac{V}{R} \][/tex]
If the resistance [tex]\( R \)[/tex] is constant and the voltage [tex]\( V \)[/tex] increases, then the current [tex]\( I \)[/tex] must increase. Therefore, this statement is True.
5. If the voltage increases, then the current decreases. Assume resistance is constant.
Using Ohm’s Law:
[tex]\[ I = \frac{V}{R} \][/tex]
If the resistance [tex]\( R \)[/tex] is constant and the voltage [tex]\( V \)[/tex] increases, then the current [tex]\( I \)[/tex] must also increase, not decrease. Therefore, this statement is False.
Thus, the two true statements are:
- Statement 2: If the resistance decreases, then the current increases. Assume voltage is constant.
- Statement 4: If the voltage increases, then the current increases. Assume resistance is constant.
The true statements are:
[tex]\[ \boxed{[2, 4]} \][/tex]
