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If the voltage across a fixed resistor is doubled, the power dissipated in the resistor will:
Double
Increase by factor of 4
Decrease by half
Remain unchanged
Increase by factor of 4
When the voltage across a fixed resistor is doubled, the power dissipation increases by a factor of four. This is because power in a resistive circuit is proportional to the square of the applied voltage.
When the voltage across a fixed resistor is doubled, the power dissipation increases by a factor of four. This is because power in a resistive circuit is proportional to the square of the applied voltage.
P=RV2тАЛ тАФ Power formula in terms of voltage and resistance
PтА▓=R(2V)2тАЛ=4P тАФ Relation showing power increase when voltage is doubled
According to Joule's Law of heating, power dissipation is given by P=RV2тАЛ. Since R is constant, P is directly proportional to V2. Therefore, if the voltage V becomes 2V, the new power PтА▓ becomes R(2V)2тАЛ=4├ЧRV2тАЛ=4P.
Power dissipated in a resistor is proportional to the square of the voltage.
Ohm's law V=IR holds constant for linear resistors.
The doubling of voltage also causes the current to double, contributing to the four-fold power increase.
Predictable power scaling in linear loads.
Standardized analysis for circuit protection.
Risk of thermal runaway if components are not rated for the 4x power increase.
Non-linear heating effects at high power levels.
Design of heating elements.
Voltage regulation and load testing in electrical systems.
The relationship PтИЭV2 is specific to resistive loads where R remains constant.
Option A is incorrect as it assumes a linear relationship; Option C is incorrect as it describes an inverse relationship; Option D ignores the dependency of power on voltage.
B is correct тАФ Power dissipation is proportional to the square of the voltage, meaning doubling the voltage results in a 22=4 times increase in power.
In competitive exams, always check if the load is constant resistance; if the circuit involves non-linear elements like diodes, the PтИЭV2 rule does not apply directly.