Questions: Chapter 28 HW (MP) - PHY211. MasteringPhysics: Ch 28: Quiz The 10 Ω resistor in (Figure 1) is dissipating 20 W of power Part A How much power is the 5 Ω resistor dissipating? Express your answer with the appropriate units. Part B How much power is the 20 Ω resistor dissipating? Express your answer with the appropriate units.

Solution Steps

We are given that a $10 \, \Omega$ resistor is dissipating $20 \, \text{W}$ of power. We need to find out how much power the $5 \, \Omega$ resistor is dissipating.

The power dissipated by a resistor can be calculated using the formula: \[ P = I^2 R \] where \( P \) is the power, \( I \) is the current, and \( R \) is the resistance. For the $10 \, \Omega$ resistor: \[ 20 = I^2 \times 10 \] \[ I^2 = \frac{20}{10} = 2 \] \[ I = \sqrt{2} \approx 1.4142 \, \text{A} \]

Using the same formula for power: \[ P = I^2 R \] For the $5 \, \Omega$ resistor: \[ P = (1.4142)^2 \times 5 \] \[ P = 2 \times 5 = 10 \, \text{W} \]

Final Answer