Answer :
To find the power dissipated by a resistor in a circuit, we can use the formula:
[tex]\[ P = I^2 \cdot R \][/tex]
where:
- [tex]\(P\)[/tex] is the power dissipated in watts (W),
- [tex]\(I\)[/tex] is the current in amperes (A),
- and [tex]\(R\)[/tex] is the resistance in ohms (Ω).
Given:
- The resistance [tex]\( R = 75 \Omega \)[/tex],
- and the current [tex]\( I = 2.0 A \)[/tex],
We will substitute these values into the formula to find the power [tex]\( P \)[/tex]:
1. First, square the current:
[tex]\[ I^2 = (2.0 \, A)^2 = 4.0 \, A^2 \][/tex]
2. Next, multiply the squared current by the resistance:
[tex]\[ P = I^2 \cdot R = 4.0 \, A^2 \cdot 75 \, \Omega \][/tex]
3. Perform the multiplication:
[tex]\[ P = 4.0 \cdot 75 = 300 \, W \][/tex]
Therefore, the power dissipated by the resistor is:
[tex]\[ 300 \, W \][/tex]
So, the correct answer is:
B. [tex]\(300 \, W\)[/tex]
[tex]\[ P = I^2 \cdot R \][/tex]
where:
- [tex]\(P\)[/tex] is the power dissipated in watts (W),
- [tex]\(I\)[/tex] is the current in amperes (A),
- and [tex]\(R\)[/tex] is the resistance in ohms (Ω).
Given:
- The resistance [tex]\( R = 75 \Omega \)[/tex],
- and the current [tex]\( I = 2.0 A \)[/tex],
We will substitute these values into the formula to find the power [tex]\( P \)[/tex]:
1. First, square the current:
[tex]\[ I^2 = (2.0 \, A)^2 = 4.0 \, A^2 \][/tex]
2. Next, multiply the squared current by the resistance:
[tex]\[ P = I^2 \cdot R = 4.0 \, A^2 \cdot 75 \, \Omega \][/tex]
3. Perform the multiplication:
[tex]\[ P = 4.0 \cdot 75 = 300 \, W \][/tex]
Therefore, the power dissipated by the resistor is:
[tex]\[ 300 \, W \][/tex]
So, the correct answer is:
B. [tex]\(300 \, W\)[/tex]
