Tag: thermal effect of electric current

Energy consumed is given by:

Resistance of Ist bulb $={ R } _{ 1 }=\cfrac { { V }^{ 2 } }{ { P } _{ 1 } } $
Resistance of IInd bulb $={ R } _{ 2 }=\cfrac { { V }^{ 2 } }{ { P } _{ 2 } } $
when both bulbs are connected in series
$\quad { R } _{ eq }={ V }^{ 2 }\left[ \cfrac { 1 }{ { P } _{ 1 } } +\cfrac { 1 }{ { P } _{ 2 } }  \right] =\cfrac { { V }^{ 2 }\left( { P } _{ 1 }+{ P } _{ 2 } \right)  }{ { P } _{ 1 }{ P } _{ 2 } } $
Hence, power consumed $P=\cfrac { { V }^{ 2 } }{ R } =\cfrac { { V }^{ 2 } }{ { V }^{ 2 }\left( \cfrac { { P } _{ 1 }+{ P } _{ 2 } }{ { P } _{ 1 }{ P } _{ 2 } }  \right)  } =\cfrac { { P } _{ 1 }{ P } _{ 2 } }{ { P } _{ 1 }+{ P } _{ 2 } } \quad $

Power consumed by bulb is $P=\dfrac{V^2}{R}$

Power of heater $=P=\dfrac{V^2}{R}$

Answer is A.

The heat which is produced due to the flow of  current   within an electric wire, is expressed in Joules.
James Prescott Joule was an English physicist who studied the nature of heat and established its relationship to mechanical work. He therefore laid the foundation for the theory of conservation of energy, which later influenced the First Law of Thermodynamics. He also formulated the Joules laws which deal with the transfer of energy.

If an electric fan is switched on in a closed room, the air will be heated because due to motion of the fan, the speed of air molecules will increase. In fact, we feel cold due to evaporation of our sweat

Laws of heating were given by Joule.

By Joule's Law, heat produced

According to Joule's law,       $W = JQ$