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If the resistance R is constant and the voltage V across a resistor is tripled, how does the power P change?
It increases by nine times.
It increases by one-third of its original.
It increases by three times.
It decreases by three times.
It increases by nine times.
When the resistance R remains constant, electrical power P is directly proportional to the square of the voltage V. Consequently, if the voltage is tripled, the power increases by a factor of 32, which equals 9.
When the resistance R remains constant, electrical power P is directly proportional to the square of the voltage V. Consequently, if the voltage is tripled, the power increases by a factor of 32, which equals 9.
Think of a water pipe where voltage is the water pressure; if you triple the pressure, the flow (current) also triples, resulting in nine times the total work output (power) at the nozzle.
P=RV2тАЛ тАФ Power formula in terms of Voltage and Resistance
P=I2R тАФ Power formula in terms of Current and Resistance
According to Joule's Law of heating and the definition of electric power, P=VI. Substituting Ohm's law, I=RVтАЛ, into the power equation yields P=RV2тАЛ. Since R is constant, P scales with V2. Tripling V results in (3V)2=9V2, indicating that power becomes nine times the original value.
Power is directly proportional to the square of the voltage when resistance is constant.
If voltage is doubled, power increases by 22=4 times.
If voltage is tripled, power increases by 32=9 times.
Useful for calculating heat dissipation in electrical circuits
Applicable only when R is constant (Ohmic resistors)
Electric heating elements
Incandescent bulb brightness
The constant of proportionality is R1тАЛ.
Option B is incorrect because power does not change linearly with voltage.
Option C is incorrect as it ignores the squaring effect in the V2 term.
A is correct тАФ Since PтИЭV2, tripling the voltage results in a power increase of 32=9 times.
Always verify if the variable being held constant is resistance or current before choosing between P=RV2тАЛ and P=I2R.
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