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Multiple choice physics alternating current power in ac circuits average power in ac circuit and power factor power in ac circuit

The current which does not contribute to the power consumed in an AC circuit is called:

  1. Non-ideal current

  2. Wattless current

  3. Convectional current

  4. Inductance current
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Wattless current does not contribute to the mean rate of working of the circuit.
As, power factor $= \frac{\text{true power}}{\text{apparent power}}$
                             $=cos\phi$
                             $=\frac{R}{\sqrt{R^2+(X _L-X _C)^2}}$
$\therefore$ Power factor $=cos\phi = \frac{R}{Z}$
In a non-inductive circuit, $X _L=X _C$
$\therefore$ Power factor $=cos\phi = \frac{R}{\sqrt{R^2}}=\frac{R}{R}=1$
$\therefore \phi = 0^o$
This is the maximum value of power factor. Iris a pure inductor or an ideal capacitor 
$\phi = 90^o$
$\therefore$ Power factor $= cos \phi = cos 90^o= 0$. 
Average power consumed in a pure inductor orb ideal capacitor 
$P = E _V \cdot I _V cos\, 90^o = zero$.
Therefore, current through pure L or pure C; which consumes no power for its maintenance in the circuit is called ideal current or wattless current.

Multiple choice physics alternating current power in ac circuits average power in ac circuit and power factor power in ac circuit

The power loss is less in transmission lines, when :

  1. Voltage is less but current is more

  2. Both voltage and current are more

  3. Voltage is more but current is less

  4. Both voltage and current are less
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The power cables have some resistance. 

Power lost in the wires can be calculated as $P=I^2R$ with $R$ as the resistance of the wires and $I$ as the current that passes through them.
Power at the load is $P=VI$. 
From this one can see that if  voltage is increased by say $n$ times, then only $\dfrac{1}{n}$ the current is required to deliver the same power. However, if $\dfrac{1}{n}$ current is passed on the same wires, only $\dfrac{1}{n^2}$ of the power will be lost.

Multiple choice physics alternating current power in ac circuits average power in ac circuit and power factor power in ac circuit

If $V=100 \sin 100t$ volt, and $I=100 \sin(100t+\dfrac {\pi}{6})A$. then find the watt less power in watt?

  1. $10^{4}$

  2. $10^{3}$

  3. $10^{2}$

  4. $2.5 \times 10^{3}{\sqrt{3}}$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

$P= V _{rms} \times I _{rms} \times \cos \phi$


$\quad= \large\frac{V _0I _0}{\sqrt{2}\times \sqrt{2}}\times \cos \dfrac{\pi}{6}$

$\quad= \large\frac{100 \times 100}{2} \times \frac{\sqrt{3}}{2}=2.5\times 10^3\sqrt{3}W$

Multiple choice physics alternating current power in ac circuits average power in ac circuit and power factor power in ac circuit

In a series $LCR$ circuit $K=200\ \Omega$ and the voltage and frequency of the main supply are $220\ V$ and $50\ Hz$ respectively. On taking out the capacitor from the circuit, the current leads the voltage by ${30}^{o}$. On taking out the indicator from the circuit the current leads the voltage by ${30}^{o}$. The power dissipated in the $LCR$ circuit is :

  1. $342\ W$

  2. $305\ W$

  3. $209\ W$

  4. $242\ W$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

$P=\cfrac { { V } _{ rms }^{ 2 } }{ R } cos\phi =\cfrac { { 220 }^{ 2 } }{ 200 } cos30°=209W$

Multiple choice physics alternating current power in ac circuits average power in ac circuit and power factor power in ac circuit

In a series LCR circuit,the inductive reactance is twice the resistance and the capacitance reactance is ${\frac{1}{3}^{rd}}$ the inductive reactance. The power factor of the circuit is:

  1. $0.5$

  2. $0.6$

  3. $0.8$

  4. $1$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

$\begin{array}{l}\omega L = 2R\\frac{1}{{\omega C}} = \frac{1}{3}\left( {\omega L} \right)\\omega L - \frac{1}{{\omega C}} = 2R - \frac{{2R}}{3} = \frac{{4R}}{3}\\tan \phi  = \frac{{4R}}{3} \times \frac{1}{R} = \frac{4}{3}\\cos \phi  = \frac{1}{{\sqrt {1 + {{\tan }^2}\phi } }} = \frac{1}{{\sqrt {1 + \frac{{{4^2}}}{{{3^2}}}} }} = \frac{3}{5} = 0.6\end{array}$

Multiple choice physics alternating current power in ac circuits average power in ac circuit and power factor power in ac circuit

An alternative current, L.R circuit comprises of an inductor, whose reactance $X _L = 3R$, where $R$ is the resistance of the circuit. If a capacitor, whose reactance $X _C = R$ is connected in series then what will be the ratio of the new and the old power factor?

  1. $\sqrt{2}$

  2. $\dfrac{1}{\sqrt{2}}$

  3. $2$

  4. $1$
Reveal answer Fill a bubble to check yourself
B Correct answer
Multiple choice physics alternating current power in ac circuits average power in ac circuit and power factor power in ac circuit

In an $LR$-circuit, the inductive reactance is equal to the resistance $R$ of the circuit. an e.m.f. $E=E _{0}\ cos(\omega t)$ applied to the circuit. The power consumed in the circuit is

  1. $\dfrac{E^{2} _{0}}{R}$

  2. $\dfrac{E^{2} _{0}}{2R}$

  3. $\dfrac{E^{2} _{0}}{4R}$

  4. $\dfrac{E^{2} _{0}}{8R}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

In an LR circuit, Z = sqrt(R^2 + XL^2). Given XL = R, Z = sqrt(2)R. Current amplitude I0 = E0 / Z = E0 / (sqrt(2)R). Average power P = (1/2) * I0^2 * R = (1/2) * (E0^2 / 2R^2) * R = E0^2 / 4R.

Multiple choice physics alternating current power in ac circuits average power in ac circuit and power factor power in ac circuit

In general in an alternating current circuit for a complete cycle

  1. The average value of current is zero

  2. The average value of square of the current is zero

  3. Average power dissipation is zero

  4. All of these
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

In an AC circuit, the current is sinusoidal, so its average value over a complete cycle is zero. The average of the square of the current is not zero (it is I_rms^2), and average power is not necessarily zero (unless the circuit is purely reactive).