Question

An X-ray tube is operating at 150kV and 19mA. If only 1% of the electrical power is converted into X-rays, the rate at which the target is heated, in $cal{{s}^{-1}}$, is
A. 3.57
B. 35.7
C. 4.57
D.15

Answer 1

Hint: An x-ray tube is a vacuum tube in which there is cathode and anode respectively. The cathode is used to heat up the element, and at anode the high velocity electrons collide. The electrical power is calculated by the product of current and potential difference.

Formula used:
Power is given as:
$P=V\times I$

Complete answer:
An x-ray tube is a vacuum tube, in which the electrical energy is converted into x-rays. The energy of X-rays depends on the kinetic energies of the respective electrons in the tube. It is made of Pyrex glass.
It has a cathode and anode inside it. Cathode is the negatively charged electrode and anode is positively charged electrode. It produces x-rays by accelerating electrons to high-voltage and causes them to collide at the target.
The formula for the electrical power is equivalent to the ohm’s law. As in ohm’s law, the voltage is given by, $V=IR$. Also, power is given by formula, $P=IV$
The electrical power is the amount of energy consumed per unit time. The amount of energy consumed depends on the current flowing in the tube.
The electrical power depends on the nature of current flowing.
The S.I unit of electrical energy is joules.
Now, in the question it is given that only 1% of electrical power is used to generate x-rays. Therefore, the 99% of the energy is used to heat up the filament. So, the power is given by:
 $\begin{align}
  & P=VI \\
 & P=150\times {{10}^{3}}\times 10\times {{10}^{-3}} \\
 & P=1500W \\
\end{align}$
Now the rate of at which target heat is given by:
$\begin{align}
  & {{H}_{p}}=(1/100)\times 1500 \\
 & {{H}_{p}}=15\times 1W \\
 & {{H}_{p}}=15W \\
 & {{H}_{p}}=15J{{s}^{-1}} \\
\end{align}$
Now, we will convert joules per sec. into calories per sec. then we have,
$1J=1/4.2(calories)$
Therefore, rate of heat is given by:
$\begin{align}
  & {{H}_{p}}=15/4.2 \\
 & {{H}_{p}}=3.57cal{{s}^{-1}} \\
\end{align}$

Hence, option A is the correct answer.

Note:
The electrical power is the amount of energy used in the circuit. An x-ray tube is a vacuum tube containing cathode and anode electrode having negative and positive type of charge on it. The power used for heating of the filament is given by product of current and potential difference.