Correct Answer - Option 2 : 0.86 leading
Concept:
Voltage regulation is the change in secondary terminal voltage from no load to full load at a specific power factor of load and the change is expressed in percentage.
E2 = no-load secondary voltage
V2 = full load secondary voltage
Voltage regulation for the transformer is given by the ratio of change in secondary terminal voltage from no load to full load to no load secondary voltage.
Voltage regulation \(= \frac{{{E_2} - {V_2}}}{{{E_2}}}\)
It can also be expressed as,
Regulation \(= \frac{{{I_2}{R_{02}}\cos {ϕ _2} \pm {I_2}{X_{02}}\sin {ϕ _2}}}{{{E_2}}}\)
+ sign is used for lagging loads and
- ve sign is used for leading loads
Hence voltage regulation can be negative only for capacitive loads
In transformer minimum voltage regulation occurs when the power factor of the load is leading.
The voltage regulation of the transformer is zero at a leading power factor load such as a capacitive load.
For zero voltage regulation, \({E_2} = {V_2}\)
\( \Rightarrow IR\cos ϕ = IX\sin ϕ \) (negative sign represents leading power factor loads)
\( \Rightarrow ϕ = {\tan ^{ - 1}}\left( {\frac{R}{X}} \right)\)
\(\cos ϕ = \cos {\tan ^{ - 1}}\left( {\frac{R}{X}} \right)\)
This is the leading power factor at which voltage regulation becomes zero while supplying the load.
Calculation:
Given that, impedance drop = IZ = VZ = 20 V
Resistance drop = IR = VR = 10 V
Hence, Reactance Drop = IX = VX = \(\sqrt{V_Z^2-V_R^2}=\sqrt{20^2-10^2}=\sqrt{300}\)
At zero regulation,
VR cos ϕ = VX sin ϕ
or, tan ϕ = \(\frac{V_R}{V_X}=\frac{10}{\sqrt{300}}=\frac{1}{\sqrt{3}}\)
\(ϕ = {\tan ^{ - 1}}\frac{{1}}{{\sqrt3}} = 30^\circ \)
Power factor = cos ϕ = 0.866 leading
