Sure, I can help you solve this problem step by step.
The relationship between voltage, current, and resistance in an electrical circuit is described by Ohm's Law. Ohm's Law states that:
[tex]\[ V = I \times R \][/tex]
where:
- [tex]\( V \)[/tex] is the voltage across the resistor (in volts, V),
- [tex]\( I \)[/tex] is the current flowing through the resistor (in amperes, A),
- [tex]\( R \)[/tex] is the resistance of the resistor (in ohms, [tex]\( \Omega \)[/tex]).
Given:
- The resistance ([tex]\( R \)[/tex]) is [tex]\( 22.5 \ \Omega \)[/tex],
- The current ([tex]\( I \)[/tex]) is [tex]\( 0.2 \)[/tex] A.
To find the voltage ([tex]\( V \)[/tex]), we substitute the given values into the formula:
[tex]\[ V = I \times R \][/tex]
[tex]\[ V = 0.2 \ \text{A} \times 22.5 \ \Omega \][/tex]
By performing the multiplication:
[tex]\[ V = 4.5 \ \text{V} \][/tex]
So, the voltage needed to drive the current of 0.2 A through a bulb with a resistance of 22.5 ohms is [tex]\( 4.5 \)[/tex] volts.
