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

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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(*wt* – *θ*), what does *i* indicate?

a) Instantaneous value

b) RMS value

c) Maximum value

d) Average value

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Explanation: A sinusoidal current wave is given by

*i*= I

_{m}sin(

*wt*–

*θ*) 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

View Answer

Explanation: A voltage sine wave is given by

*v*=V

_{m}sin

*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(*wt* – *θ*), what does I indicate?

a) Instantaneous current

b) RMS current

c) Maximum current

d) Average current

View Answer

Explanation: The equations of voltage sine wave and current sine wave are given by

*v*=V

_{m}sin

*wt*and

*i*= I

_{m}sin(

*wt*–

*θ*) respectively. In these equations I

_{m}signify the maximum current of current. Again RMS currents is given by I

_{RMS}=I

_{m}/\(\sqrt2\). On substituting the maximum current with RMS component, we get the equation

*i*= \(\sqrt2\)I

_{RMS}sin(

*wt*–

*θ*). 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(*wt* – *θ*), 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

View Answer

Explanation: The equations of voltage sine wave and current sine wave can be given by

*v*=V

_{m}sin

*wt*and

*i*= I

_{m}sin(

*wt*–

*θ*) 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(*wt* – *θ*), *θ* is in _______

a) radian

b) radian per second

c) degree

d) degree per second

View Answer

Explanation: The equations of voltage sine wave and current sine wave are given

*v*= \(\sqrt2\)V

_{RMS}sin

*wt*and

*i*= \(\sqrt2\)I

_{RMS}sin(

*wt*–

*θ*) 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(*wt* – *θ*); *wt* is in _______

a) radian

b) radian per second

c) degree

d) degree per second

View Answer

Explanation: The equations of voltage sine wave and current sine wave are given by

*v*= V

_{m}sin

*wt*and

*i*= I

_{m}sin(

*wt*–

*θ*) respectively. Also we can write these equations as

*v*= \(\sqrt2\)V

_{RMS}sin

*wt*and

*i*= \(\sqrt2\)I

_{RMS}sin(

*wt*–

*θ*) 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(*wt* – *θ*); the unit of *w* is _______

a) radian

b) radian per second

c) degree

d) degree per second

View Answer

Explanation: The equations of voltage sine wave and current sine wave are given by

*v*= V

_{m}sin

*wt*and

*i*= I

_{m}sin(

*wt*–

*θ*) respectively. Also we can write these equations as

*v*= \(\sqrt2\)V

_{RMS}sin

*wt*and

*i*= \(\sqrt2\)I

_{RMS}sin(

*wt*–

*θ*) 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(*wt* – *θ*), what does cos*θ* indicate?

a) power factor

b) angle between inductance and resistance

c) phase angle between current and voltage

d) angle between capacitance and resistance

View Answer

Explanation: The equations of voltage sine wave and current sine wave can be given by

*v*= V

_{m}sin

*wt*and

*i*= I

_{m}sin(

*wt*–

*θ*) respectively. Also we can write these equations as

*v*= \(\sqrt2\)V

_{RMS}sin

*wt*and

*i*= \(\sqrt2\)I

_{RMS}sin(

*wt*–

*θ*) 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 cos

*θ*. Broadly speaking to improve this cos

*θ*or power transmission system, the engineers are constantly working.

10. In the equations *v* = \(\sqrt2\)V sin *wt* and *i* = \(\sqrt2\)I sin(*wt* – *θ*); we find that cos*θ* is _______

a) in ampere

b) in volt

c) in degree

d) unitless

View Answer

Explanation: The equations of voltage sine wave and current sine wave are given by

*v*= V

_{m}sin

*wt*and

*i*= I

_{m}sin(

*wt*–

*θ*) respectively; or as

*v*= \(\sqrt2\)V

_{RMS}sin

*wt*and

*i*= \(\sqrt2\)I

_{RMS}sin(

*wt*–

*θ*) 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, cos

*θ*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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