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If the current through a resistor is tripled while the resistance remains constant, the power consumed becomes ______.
3 times
6 times
9 times
12 times
9 times
The power consumed by a resistor is directly proportional to the square of the current flowing through it. When the current (I) is tripled, the power (P) becomes 32 or 9 times the original value.
The power consumed by a resistor is directly proportional to the square of the current flowing through it. When the current (I) is tripled, the power (P) becomes 32 or 9 times the original value.
Think of a garden hose: if you force water through it three times as fast (like current), the friction against the pipe walls (resistance) creates significantly more turbulence and heat, specifically scaling by the square of the velocity.
PI squared R (Power is I2R)
P=I2R тАФ Power in terms of current and resistance
P=RV2тАЛ тАФ Power in terms of voltage and resistance
According to Joule's law of heating, the power dissipated in a resistor with constant resistance (R) is given by P=I2R. If the new current is IтА▓=3I, the new power becomes PтА▓=(3I)2R=9I2R. Thus, the power increases by a factor of 9.
Power consumption is sensitive to current changes due to the squared term.
Resistance (R) remains constant in this scenario, meaning the relationship between P and I is purely quadratic.
This principle is the basis for understanding why high-voltage power lines minimize energy loss (I2R loss) by reducing current.
Predictive modeling for electrical circuits
Energy efficiency optimization
Does not account for temperature-dependent resistance changes in real-world scenarios
Electric heaters
Incandescent bulbs
Fuses and circuit breakers
Joule heating is a dissipative process where electrical energy is converted into thermal energy.
Option B (6 times) is a common trap for students who mistakenly use P=2IR or P=I├ЧR instead of the square.
C is correct тАФ Since power is proportional to the square of the current (PтИЭI2), tripling the current results in 32=9 times the power.
Always identify which variable is held constant; if Voltage (V) were constant instead of Resistance (R), tripling current would imply changing R, altering the power calculation to P=VI.