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
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
Solution
Solution Steps
Step 1: Understanding Power in a Resistor
The power P dissipated by a resistor can be calculated using the formula:
P=I2R
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=RV2
Step 2: Analyzing Each Option
Doubling the current while doubling the resistance:
New power: P′=(2I)2×2R=4I2×2R=8IR
This results in an 8-fold increase in power, not just doubling.
Doubling the current by making a resistance half as big:
New resistance: R′=2R
New power: P′=(2I)2×2R=4I2×2R=2I2R
This results in a doubling of the power.
Doubling the current by doubling the voltage:
New voltage: V′=2V
New power: P′=2V×2I=4VI
This results in a 4-fold increase in power, not just doubling.
Doubling the current while making the voltage half as big:
New voltage: V′=2V
New power: P′=2V×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