A resistor develops 300 J of thermal energy is 15 s , when a current of 2 A is passed through it. If

Question

A resistor develops 300 J of thermal energy is 15 s , when a current of 2 A is passed through it. If the current increases to 3 A , the energy developed in 10 s is ____ J.\

Professor PC Thomas Classes · Answer

(450) : Here, Heat, $H=300 \mathrm{~J}$;\ time, $t=15 \mathrm{~s}$; current, $i=2 \mathrm{~A}$\ New current, $i^{\prime}=3 \mathrm{~A}$, New time, $t^{\prime}=10 \mathrm{~s}$ $$\begin{equation*} H=i^{2} R t 	ag{i} \end{equation*}$$$$\begin{equation*} H^{\prime}=i^{\prime 2} R t^{\prime} 	ag{ii} \end{equation*}$$ Divide eq. (i) by (ii), we get\ $\frac{300}{H^{\prime}}=\left(\frac{2}{3}ight)^{2} 	imes \frac{15}{10} ;$\ $\frac{300}{H^{\prime}}=\frac{4}{9} 	imes \frac{15}{10} ; H^{\prime}=\frac{300 	imes 9 	imes 10}{4 	imes 15}$;\ Thus, $H^{\prime}=450 \mathrm{~J}$\