Chapter 25, Problem 92A

(a)

To determine

To write:

The expression for the efficiency of the transformer in percent using the power relationship.

Answer to Problem 92A

The expression for the efficiency of power is Efficiency $e=\frac{P_s}{P_p}\times 100$ .

Explanation of Solution

Given:

For a step down transformer:

Efficiency: $92.5\%$

Voltage of secondary $V_s$ : $28.0$ V

Voltage of primary $V_p$ : $125$ V

Current: $25.0$ A

Formula used:

The formula to calculate the efficiency of power for transformer is given by,

  $e=\frac{P_s}{P_p}\times 100$

Where,

  $P_s$ : Secondary Power

  $P_p$ : Primary Power

  $e$ : Efficiency

Calculation:

To write the expression of the efficiency of transformer in percent, it is written as

  $e=\frac{P_s}{P_p}\times 100$

Where,

  $P_s$ : Secondary Power

  $P_p$ : Primary Power

  $e$ : Efficiency

Conclusion:

The expression for the efficiency of power is Efficiency $e=\frac{P_s}{P_p}\times 100$ .

(b)

To determine

To calculate:

The current in the primary circuit.

Answer to Problem 92A

The current in the primary circuit is $6.05A$ .

Explanation of Solution

Given:

For a step down transformer:

Efficiency: $92.5\%$

Voltage of secondary $V_s$ : $28.0$ V

Voltage of primary $V_p$ : $125$ V

Current: $25.0$ A

Formula used:

For the secondary power

  $P_s=V_s{I}_s$

For the primary current,

  $I_p=\frac{P_p}{V_p}$

Where,

  $V_s$ : Voltage of secondary

  $I_p$ : Primary Current

  $V_p$ : Voltage of primary

  $P_s$ : Secondary power

Calculation:

In the First step calculate the secondary power and primary power to find the primary current,

Secondary power is given by the formula,

  $P_s=V_s{I}_s$

Substitute all the given values in the above formula,

  $=\left(28.0\right)\times \left(25.0\right)$

  $P_s$ = $7.00\times {10}^2$ W

Secondary power is $7.00\times {10}^2$ W

Now calculate the primary power, which is given by the formula,

  $P_p=\frac{\left(100\right)\times P_s}{e}$

Substitute all the given values in the above formula,

  $=\frac{\left(100\right)\times \left(7.00\times {10}^2\right)}{92.5}$ = $757$ W

  $P_p=757$ W

Primary power is $757$ W

Now in the last step the primary current is found,

The formula for primary current is given by,

  $I_p=\frac{P_p}{V_p}$

Substituting all the given values in the above formula

  $I_p=(\frac{757}{125})$ W= $6.05$ A

  $I_p=6.05$ A

Conclusion:

Hence the current in the primary circuit is $6.05$ A.

(c)

To determine

To calculate:

Therate of thermal energy generated.

Answer to Problem 92A

Thermal energy will be produced at the rate of 57 J/s. This is the difference between the input power (757 W) and the output power (700 W)

Explanation of Solution

thermal energy can be calculated by taking the difference between the Input power that is the primary power and the output power that is the secondary power.

From the above calculation,

Input power $=$ $757$ W

Output Power $=$ $700$ W

Thermal Energy= Input Power- Output Power

  = $(757-750)$ W

  = $57$ W

Conclusion:

Hence the rate at which thermal energy is generated is $\begin{array}{l}57\\ \end{array}$ W.