How much voltage is required to run 0.64 A of current through a [tex]$240 \Omega$[/tex] resistor? Use [tex]\Delta V = I R[/tex].

A. [tex]2.7 \times 10^{-3} V[/tex]
B. [tex]1.5 \times 10^2 V[/tex]
C. [tex]3.8 \times 10^2 V[/tex]
D. [tex]6.5 \times 10^{-3} V[/tex]



Answer :

To solve this problem, we will use Ohm's Law, which states that the voltage [tex]\( \Delta V \)[/tex] across a resistor is the product of the current [tex]\( I \)[/tex] flowing through the resistor and the resistance [tex]\( R \)[/tex] of the resistor. The formula is given by:

[tex]\[ \Delta V = I \cdot R \][/tex]

Here, the given values are:
- Current ([tex]\( I \)[/tex]) = 0.64 A
- Resistance ([tex]\( R \)[/tex]) = 240 Ω

We can substitute these values into the formula to find the voltage:

[tex]\[ \Delta V = 0.64 \, \text{A} \times 240 \, \Omega \][/tex]

Performing the multiplication, we get:

[tex]\[ \Delta V = 153.6 \, \text{V} \][/tex]

Therefore, the voltage required to run 0.64 A of current through a 240 Ω resistor is [tex]\( 153.6 \, \text{V} \)[/tex].

Among the given choices, the correct option is:

B. [tex]\( 1.5 \times 10^2 \, \text{V} \)[/tex]

This notation is scientifically approximate, where [tex]\( 1.5 \times 10^2 \, \text{V} \)[/tex] equals 150 V, and the closest numerical value to our exact calculation of 153.6 V.