Question

$\Huge{\mathscr{\fcolorbox {lime}{orange}{\fcolorbox {yellow}{red}{\color {darkgreen}{Question:-}}}}$

Prove that

$\boxed{\mathscr {\purple {H=I^2Rt}}}$​

Answer 1

$\mapsto\bf{Proof}$

$\rightarrowtail$ let us consider a resistance R , in which I amount of current flows.

$\rightarrowtail$ Work must be done by current to move continuously.

$\rightarrowtail$ $\sf\color{red}W= Q x V$

$\rightarrowtail$ $\sf\color{red}BUT$

$\rightarrowtail$$\sf\color{blue}Q= IX t$

$\rightarrowtail$$\sf\color{green}W = I x V x t$

$\rightarrowtail$$\sf\color{purple}but\: from\: ohms\: law: V=IR$

$\rightarrowtail$$\sf\color{pink}W=I²Rt$

$\rightarrowtail$bassuming the electrical energy consumed is converted into heat energy .

$\rightarrowtail$ we write work done as Heat produced.

$\boxed{\bf{So,}}$

$\boxed{\mathscr {\purple {H=I^2Rt}}}$

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★$\underline{\bf{More\: info :-}}$★

$\Rrightarrow$$\underline{\bf{Q}}$= Amount of heat

$\Rrightarrow$$\underline{\bf{I}}$= Electric current

$\Rrightarrow$$\underline{\bf{R}}$ = Amount of electric resistance in the conductor

$\Rrightarrow$$\underline{\bf{T}}$ = Time

Thankyou :)

Answer 2

To prove : H = I²Rt

Heat is a form of energy and is possessed by a body due to the vibratory motion of its molecule.

Joule's Law of Heating states that when heat produced in the conductor is equal to the product of the resistance, time and square of current.

We know,

$\boxed{\sf {Q=It}}$

$\boxed{\sf V= \dfrac{W}{Q}}$ – [a]

By putting the value of Q in equation [a],

$\boxed{\sf V = \dfrac{W}{It}}$

$\boxed{\sf {W=VIt}}$ – [b]

According to Ohm's Law,

$\boxed{\sf {V=IR}}$

By putting the value of V in equation [b],

$\boxed{\sf {W=(IR)It}}$

$\boxed{\sf {W=I^2Rt}}$

Therefore, $\boxed{\sf {H=I^2Rt}}$

Hence Proved!