# FACTS Questions and Answers – Power Flow in AC Power System – Set 2

This set of FACTS Multiple Choice Questions & Answers (MCQs) focuses on “Power Flow in AC Power System – Set 2”.

1. The full form of UPS is ________
a) Uninterrupted Power Supply
b) Unique Power Supply
c) Unified Power Supply
d) Uninterrupted Power Surge

Explanation: The full form of UPS is Uninterrupted Power Supply. Uninterruptible Power Supplies (UPS) and voltage regulators represent a major growth and application area in power electronics.

2. In the equation i = $$\sqrt2$$I sin(wtθ), what does i indicate?
a) Instantaneous value
b) RMS value
c) Maximum value
d) Average value

Explanation: A sinusoidal current wave is given by i = Im sin(wtθ) Here i is the instantaneous value of current. In the sinusoidal wave the current does changes its value every instant. So it is called instantaneous current. It finds application in AC power transmission systems.

3. In the equation v = V sin wt, what does v indicate?
a) Instantaneous value
b) RMS value
c) Maximum value
d) Average value

Explanation: A voltage sine wave is given by v =Vmsin wt. In this equation v is the instantaneous value of the voltage. In the sinusoidal wave the voltage does changes its value every instant. So it is called instantaneous voltage. It finds application in AC power transmission systems.

4. In the equations v = $$\sqrt2$$V sin wt and i = $$\sqrt2$$I sin(wtθ), what does I indicate?
a) Instantaneous current
b) RMS current
c) Maximum current
d) Average current

Explanation: The equations of voltage sine wave and current sine wave are given by v =Vmsin wt and i = Im sin(wtθ) respectively. In these equations Im signify the maximum current of current. Again RMS currents is given by IRMS=Im/$$\sqrt2$$. On substituting the maximum current with RMS component, we get the equation i = $$\sqrt2$$IRMS sin(wtθ). Hence in the given equation I indicates RMS current, not otherwise. We use this RMS value in various calculations of power in ac circuits.

5. In the equations v = V sin wt and i = I sin(wtθ), what does θ indicate?
a) power factor
b) angle between inductance and resistance
c) phase angle between current and voltage
d) angle between capacitance and resistance

Explanation: The equations of voltage sine wave and current sine wave can be given by v =Vmsin wt and i = Im sin(wtθ) respectively. In all these θ is the angle between voltage and current. This angle θ plays a significant role in ac power transmission system. It is this angle of difference which decides how much the current is lagging or leading the voltage in ac power flow.

6. In the equations v = $$\sqrt2$$V sin wt and i = $$\sqrt2$$I sin(wtθ), θ is in _______
c) degree
d) degree per second

Explanation: The equations of voltage sine wave and current sine wave are given v = $$\sqrt2$$VRMS sin wt and i = $$\sqrt2$$IRMS sin(wtθ) respectively. In all these θ is the angle between voltage and current. θ is expressed in radian and not in degree. This angle θ indicates whether current is lagging or leading the voltage; and accordingly is positive or negative. If the value of θ is given in degree, it is to be converted to radian before inserting or substituting in the voltage or current equation.

7. In the equations v = $$\sqrt2$$V sin wt and i = $$\sqrt2$$I sin(wtθ); wt is in _______
c) degree
d) degree per second

Explanation: The equations of voltage sine wave and current sine wave are given by v = Vmsin wt and i = Im sin(wtθ) respectively. Also we can write these equations as v = $$\sqrt2$$VRMS sin wt and i = $$\sqrt2$$IRMS sin(wtθ) respectively. In all these equations wt is expressed in radian and not in degree. By virtue of definition, sine or cos can be found for that quantity which is in degree or radian. Since we consider angular quantities in sinusoidal voltage and current equations, we use radian to maintain the uniformity in calcutions. Hence wt is in radian.

8. In the equations v = $$\sqrt2$$V sin wt and i = $$\sqrt2$$I sin(wtθ); the unit of w is _______
c) degree
d) degree per second

Explanation: The equations of voltage sine wave and current sine wave are given by v = Vmsin wt and i = Im sin(wtθ) respectively. Also we can write these equations as v = $$\sqrt2$$VRMS sin wt and i = $$\sqrt2$$IRMS sin(wtθ) respectively. All these equations represent sine (or cosine) waves where we consider the angular quantities like angular velocity. The instantaneous velocity is given by w which is measured in radian per second.

9. In the equations v = V sin wt and i = I sin(wtθ), what does cosθ indicate?
a) power factor
b) angle between inductance and resistance
c) phase angle between current and voltage
d) angle between capacitance and resistance

Explanation: The equations of voltage sine wave and current sine wave can be given by v = Vmsin wt and i = Im sin(wtθ) respectively. Also we can write these equations as v = $$\sqrt2$$VRMS sin wt and i = $$\sqrt2$$IRMS sin(wtθ) respectively. All these equations representing sinusoidal waves graphically relate θ as the angle between voltage and current at every instant. By definition the power factor is given by cosθ. Broadly speaking to improve this cosθ or power transmission system, the engineers are constantly working.

10. In the equations v = $$\sqrt2$$V sin wt and i = $$\sqrt2$$I sin(wtθ); we find that cosθ is _______
a) in ampere
b) in volt
c) in degree
d) unitless

Explanation: The equations of voltage sine wave and current sine wave are given by v = Vmsin wt and i = Im sin(wtθ) respectively; or as v = $$\sqrt2$$VRMS sin wt and i = $$\sqrt2$$IRMS sin(wtθ) respectively. All these equations are the graphical representations of sinusoids. Here the units of current, voltage are ampere and volt respectively. Next the power factor, cosθ is basically a ratio and hence unit-less. It is often expressed in decimal e.g. 0.85.

Sanfoundry Global Education & Learning Series – Flexible AC Transmission System (FACTS).

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