When an X-ray tube operates at a tube voltage | vedclass

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(B) The total power input to the $X$-ray tube is $P = V 	imes I = 50 	imes 10^3 \, V 	imes 20 	imes 10^{-3} \, A = 1000 \, W$ (or $J/s$).Since the

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$236$

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(B) The total power input to the $X$-ray tube is $P = V 	imes I = 50 	imes 10^3 \, V 	imes 20 	imes 10^{-3} \, A = 1000 \, W$ (or $J/s$).Since the efficiency $\eta$ is $1 \%$,the power converted into $X$-rays is $P_{X} = 0.01 	imes 1000 = 10 \, J/s$.The remaining power is dissipated as heat: $P_{heat} = P - P_{X} = 1000 - 10 = 990 \, J/s$.To convert this into calories per second,we use the conversion factor $1 \, cal \approx 4.2 \, J$.Heat produced per second $= \frac{990}{4.2} \approx 235.7 \, cal/s \approx 236 \, cal/s$.

When an $X$-ray tube operates at a tube voltage of $50 \, kV$,the anode current is $20 \, mA$. If the efficiency of the $X$-ray production is $1 \%$,what is the heat produced per second in calories?

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