Calculate Current Using Power and Resistance

This solution explains how to find the electric Current (I) when Power (P) and Resistance (R) are given.

Identify Given Values

• Power ($P$): 100 watts
• Resistance ($R$): 4 ohms

Relevant Formula

The relationship between Power ($P$), Current ($I$), and Resistance ($R$) is given by the formula:

$ P = I^2 \times R $

Derive Formula for Current

To find the Current ($I$), we need to rearrange the formula:

1. Divide both sides by Resistance ($R$):

   $ \frac{P}{R} = I^2 $

2. Take the square root of both sides:

   $ I = \sqrt{\frac{P}{R}} $

Calculate Current

Substitute the given values into the derived formula:

$ I = \sqrt{\frac{100 \, \text{W}}{4 \, \Omega}} $

$ I = \sqrt{25 \, \text{A}^2} $

$ I = 5 \, \text{A} $

Conclusion

The calculated Current ($I$) is 5 A.