Concept explainers
A 240-V rms 60-Hz supply serves a load that is 10 kW (resistive), 15 kVAR (capacitive), and 22 kVAR (inductive). Find:
- (a) the apparent power
- (b) the current drawn from the supply
- (c) the kVAR rating and capacitance required to improve the power factor to 0.96 lagging
- (d) the current drawn from the supply under the new power-factor conditions
(a)
Find the apparent power for the given loads.
Answer to Problem 73P
The apparent power for the given loads is
Explanation of Solution
Given data:
The voltage
The Frequency
The real power
The reactive power is,
Formula used:
Write the expression to find the complex power.
Here,
Calculation:
Substitute
As the reactive power
On comparing the above equation with equation (1).
The apparent power
Conclusion:
Thus, the apparent power for the given loads is
(b)
Find the current drawn from the supply.
Answer to Problem 73P
The current drawn from the supply is
Explanation of Solution
Given data:
From Part (a), the complex power is,
The voltage
Formula used:
Write the expression to find the rms current.
Calculation:
Substitute
Convert the equation from rectangular to polar form.
Conclusion:
Thus, the current drawn from the supply is
(c)
Find the value of the capacitance and reactive power to raise the power factor to 0.96 lagging.
Answer to Problem 73P
The value of capacitance C is
Explanation of Solution
Given data:
From Part (a),
The frequency
Power factor
The rms voltage is
Formula used:
Write the expression to find the phase angle
Here,
Write the expression for phase angle
Write the expression to find the value of the capacitance.
Here,
Calculation:
Substitute
The power factor is raised to 0.96 lagging.
Substitute 0.96 for
The reactive power is calculated as follows.
Substitute
Substitute
Simplify the equation as follows,
Conclusion:
Thus, the value of capacitance C is
(d)
Find the current drawn from the supply under the new power factor condition.
Answer to Problem 73P
The current drawn from the supply is
Explanation of Solution
Given data:
The voltage
The real power is,
From Part (a),
From Part (c),
Calculation:
The complex power
The reactive power
Substitute
Substitute
Substitute
Convert the equation from rectangular to polar form.
Conclusion:
Thus, the current drawn from the supply is
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Chapter 11 Solutions
EBK FUNDAMENTALS OF ELECTRIC CIRCUITS
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