A resistor develops 500 , J of thermal energy | vedclass

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(D) The thermal energy $H$ developed in a resistor is given by the formula $H = I^2 R t$,where $I$ is the current,$R$ is the resistance,and $t$ is the

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$2000$

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(D) The thermal energy $H$ developed in a resistor is given by the formula $H = I^2 R t$,where $I$ is the current,$R$ is the resistance,and $t$ is the time.Given for the first case: $H_1 = 500 \, J$,$I_1 = 1.5 \, A$,$t = 20 \, s$.Substituting these values: $500 = (1.5)^2 	imes R 	imes 20$.$500 = 2.25 	imes R 	imes 20 \implies 500 = 45 	imes R \implies R = \frac{500}{45} = \frac{100}{9} \, \Omega$.For the second case: $I_2 = 3 \, A$,$t = 20 \, s$.The new energy $H_2$ is: $H_2 = I_2^2 	imes R 	imes t$.$H_2 = (3)^2 	imes \left(\frac{100}{9}ight) 	imes 20$.$H_2 = 9 	imes \left(\frac{100}{9}ight) 	imes 20 = 100 	imes 20 = 2000 \, J$.

$A$ resistor develops $500 \, J$ of thermal energy in $20 \, s$ when a current of $1.5 \, A$ is passed through it. If the current is increased from $1.5 \, A$ to $3 \, A$,what will be the energy (in $J$) developed in $20 \, s$?

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