Two impedance Z1 and Z2 when connected separately across a 230 V 50hz ...
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