Chapter 25, Problem 90A

(a)

To determine

To calculate:

Number of turns at primary side of dental X ray machine has.

Answer to Problem 90A

The number of turns at the primary side of dental X ray machine has is $500$ turns.

Explanation of Solution

Given:

Voltage at primary side = $240\text{V}$

Voltage at secondary side= $96,000\text{V}$

Output current= $1.0\text{mA}$

Formula used:

The formula to calculate the number of turns is given by,

  $\frac{V_s}{V_p}=\frac{N_s}{N_p}$

Where,

  $V_s$ : Voltage at secondary side

  $V_p$ : Voltage at primary side

  $N_s$ : Number of turns at primary side

  $N_p$ : Number of turns at secondary side

Calculation:

To calculate the number of turns at the primary sidethe formula used to calculate the number of turns.

  $\frac{V_s}{V_p}=\frac{N_s}{N_p}$

Now, here to get the number of turns at primary side rearrange the formula,

  $N_p=\frac{N_s{V}_p}{V_s}$

Substituting the values in the above formula,

  $=$$\frac{\left(200,000\right)\times \left(\text{240}\text{V}\right)}{\text{96,000}\text{V}}$

  $N_p$$=$ $500$ turns

Conclusion:

The number of turns at primary side of dental X ray machine has is $500$ turns.

(b)

To determine

To calculate:The input current.

Answer to Problem 90A

The input current for the dental X ray machine is $0.4\text{0}\text{A}$

Explanation of Solution

Given:

Voltage at primary side = $240\text{V}$

Voltage at secondary side= $96,000\text{V}$

Output current= $1.0\text{mA}$

Formula used:

To calculate the input current formula is,

  $V_p{I}_p=V_s{I}_s$

Where,

  $V_s$ : Voltage at secondary side

  $V_p$ : Voltage at primary side

  $I_p$ : Input current

  $I_s$ : Output current

Conversion:

  $1\text{mA}$

  $=$ $1.0\times {10}^{-3}\text{A}$

Calculation:

Now, to calculate the input current formula is given as,

  $V_p{I}_p=V_s{I}_s$

Rearrange the formula to find the value of input current,

  $I_p=\frac{V_s{I}_s}{V_p}$

Substituting the values in the above formula,

  $=$ $\frac{\left(\text{96,000}\text{V}\right)\text{×}\left(\text{1}{\text{.0×10}}^{\text{-3}}\text{A}\right)}{\text{240}\text{A}}$

  $=$$0.40\text{A}$

Conclusion:

The input current for the dental X ray machine is $0.40\text{A}$ .