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A 4Ω resistor has a specified maximum power dissipation of 784 W. Calculate its maximum current level.
Question

A 4Ω resistor has a specified maximum power dissipation of 784 W. Calculate its maximum current level.

A.

196 A

B.

10 A

C.

14 A

D.

16 A

Correct option is C

To calculate the maximum current level for a 4Ω resistor with a maximum power dissipation of 784 W, we can use the formula for power dissipation in a resistor:

P=I2RWhere: P is the power dissipation (784 W), I is the current (which we need to find), R is the resistance (4Ω).Rearranging the formula to solve for I:I=PRNow, substituting the known values:I=7844=196=14 AThus, the maximum current is 14 A.P = I^2 R \\[8pt]\text{Where:} \\[4pt]\bullet \; P \text{ is the power dissipation (784 W),} \\[4pt]\bullet \; I \text{ is the current (which we need to find),} \\[4pt]\bullet \; R \text{ is the resistance (4}\Omega\text{).} \\[8pt]\text{Rearranging the formula to solve for } I: \\[4pt]I = \sqrt{\frac{P}{R}} \\[8pt]\text{Now, substituting the known values:} \\[4pt]I = \sqrt{\frac{784}{4}} = \sqrt{196} = 14\,A \\[8pt]\text{Thus, the maximum current is } 14\,A.​​

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