Question

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

Prove that

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

Answer 1

$\mapsto\bf{Proof}$

➦ let us consider a resistance R , in which I amount of current flows.

➦ Work must be done by current to move continuously.

➦ $\sf\color{red}W= Q x V$

➦ $\sf\color{red}BUT$

➦$\sf\color{blue}Q= IX t$

➦$\sf\color{green}W = I x V x t$

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

➦$\sf\color{pink}W=I²Rt$

➦bassuming the electrical energy consumed is converted into heat energy .

➦ we write work done as Heat produced.

➦ So,

$\bold{\boxed{H=I^2Rt}}$

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$\underline{\bf{More\: info :-}}$

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

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

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

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

Thankyou :)

Answer 2

$\tt \: { \red{Proof \: for \: H=I^2Rt}}$

Consider current I flowing through a resistor of resistance R. Let the potential difference across it be V. Let T be the time during which a charge Q flows across.The work done in moving the charge through a potential difference is VQ. Therefore, the source must supply energy equal to VQ in time T. Hence, the power input to the circuit by the source is:

$\tt \: P=V \frac{ Q}{T}=VI$

Or energy supplied to the circuit by the source in time T is P×T that is,VIT. This is the energy that gets dissipated in the resistor as heat. Thus for a steady current I, the amount of heat H produced in time t is:

$\tt \: H=VIT$

Applying Ohms law,we get;

$\tt \: { {H=I^2Rt}}$

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