Questions: Which process will double the power given off by a resistor? doubling the current while doubling the resistance doubling the current by making a resistance half as big doubling the current by doubling the voltage doubling the current while making the voltage half as big

Solution Steps

The power \( P \) dissipated by a resistor can be calculated using the formula: \[ P = I^2 R \] where \( I \) is the current through the resistor and \( R \) is the resistance.

Alternatively, using Ohm's Law (\( V = IR \)), power can also be expressed as: \[ P = VI \] or \[ P = \frac{V^2}{R} \]

1. Doubling the current while doubling the resistance:

   • New power: \( P' = (2I)^2 \times 2R = 4I^2 \times 2R = 8IR \)
   • This results in an 8-fold increase in power, not just doubling.

2. Doubling the current by making a resistance half as big:

   • New resistance: \( R' = \frac{R}{2} \)
   • New power: \( P' = (2I)^2 \times \frac{R}{2} = 4I^2 \times \frac{R}{2} = 2I^2R \)
   • This results in a doubling of the power.

3. Doubling the current by doubling the voltage:

   • New voltage: \( V' = 2V \)
   • New power: \( P' = 2V \times 2I = 4VI \)
   • This results in a 4-fold increase in power, not just doubling.

4. Doubling the current while making the voltage half as big:

   • New voltage: \( V' = \frac{V}{2} \)
   • New power: \( P' = \frac{V}{2} \times 2I = VI \)
   • This results in no change in power.

Final Answer