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A transformer whose nameplate reads 2300/230 V, 25 kVA operates with primary and secondary voltages of 2300 V and 230 V rms, respectively, and can supply 25 kVA from its secondary winding. If this transformer is supplied with 2300 V rms and is connected to secondary loads requiring 8 kW at unity PF and 15 kVA at 0.8 PF lagging, (a) what is the primary current? (b) How many kilowatts can the transformer still supply to a load operating at 0.95 PF lagging?
(a)
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Find the value of primary current for the given data.
Answer to Problem 51E
The value of primary current for the given data is
Explanation of Solution
Given data:
Primary voltage of the transformer
Secondary voltage of the transformer
Apparent power can supplied by the transformer from its secondary winding
Required average power for load 1
Power factor of the load 1
Required apparent power for load 2
Power factor of the load 2
Formula used:
Write the expression transformer ratio as follows:
Here,
Write the expression transformer ratio as follows:
Here,
Write the expression for current in terms of average power and voltage as follows:
Here,
PF is the power factor.
Write the expression for current in terms of apparent power and voltage as follows:
Here,
Calculation:
Modify the expression in Equation (3) for the current drawn by the load 1 as follows:
Substitute
Modify the expression in Equation (4) for the current drawn by the load 2 as follows:
Substitute
As the secondary current of the transformer is the sum of the currents drawn by the two loads, write the expression for secondary current of the transformer as follows:
Substitute
Substitute 2300 V for
Rearrange the expression in Equation (2) for the primary current of the transformer as follows:
Substitute
Conclusion:
Thus, the value of primary current for the given data is
(b)
![Check Mark](/static/check-mark.png)
Calculate the average power can be supplied by the transformer to a load of 0.95 lagging along with the existing loads.
Answer to Problem 51E
The average power can be supplied by the transformer to a load of 0.95 lagging is
Explanation of Solution
Given data:
Consider the load operating at 0.95 lagging as load 3.
Power factor of the load 3
Formula used:
Write the expression for maximum rated secondary current of the transformer as follows:
Write the expression for average power in terms of voltage, current, and power factor as follows:
Calculation:
Substitute
From the given data, write the expression for current drawn by the load 3 as follows:
Substitute 0.95 for
Write the expression for secondary current of the transformer by considering load 3 as follows:
Substitute
The absolute value of the new secondary current of the transformer is equal to the maximum rated secondary current of the transformer. Therefore, write the expression as follows:
Substitute
Simplify the expression as follows:
Simplify the quadratic expression and find the value of current drawn by the load 3 as follows:
Ignore the negative value and consider the positive value for the current drawn by the load 3 as follows:
Modify the expression in Equation (6) for the average power that can be supplied for the load 3 along with the two loads as follows:
Substitute
Conclusion:
Thus, the average power can be supplied by the transformer to a load of 0.95 lagging is
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Chapter 13 Solutions
ENGINEERING CIRCUIT...(LL)>CUSTOM PKG.<
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