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

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
Transcript text: 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
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Solution

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Solution Steps

Step 1: Understanding Power in a Resistor

The power P P dissipated by a resistor can be calculated using the formula: P=I2R P = I^2 R where I I is the current through the resistor and R R is the resistance.

Alternatively, using Ohm's Law (V=IR V = IR ), power can also be expressed as: P=VI P = VI or P=V2R P = \frac{V^2}{R}

Step 2: Analyzing Each Option
  1. Doubling the current while doubling the resistance:

    • New power: P=(2I)2×2R=4I2×2R=8IR 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=R2 R' = \frac{R}{2}
    • New power: P=(2I)2×R2=4I2×R2=2I2R 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 V' = 2V
    • New power: P=2V×2I=4VI 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=V2 V' = \frac{V}{2}
    • New power: P=V2×2I=VI P' = \frac{V}{2} \times 2I = VI
    • This results in no change in power.

Final Answer

The process that will double the power given off by a resistor is:

doubling the current by making a resistance half as big \boxed{\text{doubling the current by making a resistance half as big}}

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