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Two impedance Z1 and Z2 when connected separately across a 230 V 50hz supply consumed 100W and 60 W at power factors of 0.5 lagging and 0.6 leading resp . If these impedances are now connected on series across same supply find: a )total power absorbed b) value of impedance to be added in series to raise overall power factor to unity?
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Problem Statement:
Two impedances, Z1 and Z2, when connected separately across a 230V 50Hz supply, consumed 100W and 60W at power factors of 0.5 lagging and 0.6 leading, respectively. If these impedances are now connected in series across the same supply, find:
a) the total power absorbed
b) the value of the impedance to be added in series to raise the overall power factor to unity.

Solution:

Given:
Supply voltage (V) = 230 V
Frequency (f) = 50 Hz
Power absorbed by impedance Z1 (P1) = 100 W
Power factor of Z1 (PF1) = 0.5 lagging
Power absorbed by impedance Z2 (P2) = 60 W
Power factor of Z2 (PF2) = 0.6 leading

Calculating Impedance:
Impedance (Z) can be calculated using the formula:

Z = V / I

Where:
Z is the impedance
V is the voltage
I is the current

Calculating Current:
The current (I) can be calculated using the formula:

I = P / (V * PF)

Where:
I is the current
P is the power
V is the voltage
PF is the power factor

Calculating Power:
The power (P) can be calculated using the formula:

P = V * I * PF

Where:
P is the power
V is the voltage
I is the current
PF is the power factor

Calculating Power Absorbed by Z1:
Using the given values:
P1 = 100 W
PF1 = 0.5 lagging
V = 230 V

We can calculate the current (I1) absorbed by Z1:

I1 = P1 / (V * PF1)
I1 = 100 / (230 * 0.5)
I1 = 0.8696 A

Calculating Power Absorbed by Z2:
Using the given values:
P2 = 60 W
PF2 = 0.6 leading
V = 230 V

We can calculate the current (I2) absorbed by Z2:

I2 = P2 / (V * PF2)
I2 = 60 / (230 * 0.6)
I2 = 0.4348 A

Calculating Total Current:
The total current (IT) can be calculated by adding the currents absorbed by Z1 and Z2:

IT = I1 + I2
IT = 0.8696 + 0.4348
IT = 1.3044 A

Calculating Total Power:
The total power (PT) absorbed by the series impedance can be calculated using the formula:

PT = V * IT
PT = 230 * 1.3044
PT = 299.7912 W

Calculating Impedance for Unity Power Factor:
To raise the overall power factor to unity, an impedance (Z3) needs to be added in series. The power factor (PF3) for unity power factor is 1.0.

Using the formula:

PF3
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Two impedance Z1 and Z2 when connected separately across a 230 V 50hz supply consumed 100W and 60 W at power factors of 0.5 lagging and 0.6 leading resp . If these impedances are now connected on series across same supply find: a )total power absorbed b) value of impedance to be added in series to raise overall power factor to unity?
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Two impedance Z1 and Z2 when connected separately across a 230 V 50hz supply consumed 100W and 60 W at power factors of 0.5 lagging and 0.6 leading resp . If these impedances are now connected on series across same supply find: a )total power absorbed b) value of impedance to be added in series to raise overall power factor to unity? for Class 12 2024 is part of Class 12 preparation. The Question and answers have been prepared according to the Class 12 exam syllabus. Information about Two impedance Z1 and Z2 when connected separately across a 230 V 50hz supply consumed 100W and 60 W at power factors of 0.5 lagging and 0.6 leading resp . If these impedances are now connected on series across same supply find: a )total power absorbed b) value of impedance to be added in series to raise overall power factor to unity? covers all topics & solutions for Class 12 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two impedance Z1 and Z2 when connected separately across a 230 V 50hz supply consumed 100W and 60 W at power factors of 0.5 lagging and 0.6 leading resp . If these impedances are now connected on series across same supply find: a )total power absorbed b) value of impedance to be added in series to raise overall power factor to unity?.
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