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Question 6a

In a simple electrical circuit, resistance [tex]R[/tex], current [tex]I[/tex], and power [tex]P[/tex] are all related. Rewrite the formula for resistance to solve for power, [tex]P[/tex].

[tex]R = \frac{P}{I^2}[/tex]

A. [tex]P = \frac{I^2}{R}[/tex]

B. [tex]P = \frac{V}{I^2}[/tex]

C. [tex]P = \frac{I \cdot R}{2}[/tex]

D. [tex]P = I^2 \cdot R[/tex]

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Sagot :

GinnyAnsweridn
Sure! Let's solve the problem step-by-step.


We are given the formula for resistance [tex]\( R \)[/tex] in terms of power [tex]\( P \)[/tex] and current [tex]\( I \)[/tex]:

[tex]\[ R = \frac{P}{I^2} \][/tex]

We need to rewrite this formula to solve for power [tex]\( P \)[/tex].

1. Start with the given equation:
[tex]\[ R = \frac{P}{I^2} \][/tex]

2. To isolate [tex]\( P \)[/tex], multiply both sides of the equation by [tex]\( I^2 \)[/tex]:

[tex]\[ R \times I^2 = \frac{P}{I^2} \times I^2 \][/tex]

3. Simplify the right side of the equation:

[tex]\[ R \times I^2 = P \][/tex]

Thus, the correct formula to solve for power [tex]\( P \)[/tex] in terms of resistance [tex]\( R \)[/tex] and current [tex]\( I \)[/tex] is:

[tex]\[ P = I^2 \cdot R \][/tex]

So, among the given options, the correct answer is:
[tex]\[ P = I^2 \cdot R \][/tex]
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