Tag: alternating current

Quizzes (2) Questions (29)

Questions Related to alternating current

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

An electrical device draws 2 kW power from ac mains voltage 223 V(rms). The current differs lags in phase by $\phi = tan^{-1} \left ( -\frac{3}{4} \right )$ as compared to voltage. The resistance R in the circuit is:

  1. 15 $\Omega$

  2. 20 $\Omega$

  3. 25 $\Omega$

  4. 30 $\Omega$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Here, $P \, = \, 2 \, kW \, = \, 2 \, \times \, 10^3W$
$V _{rms} \, = \, 233 \, V, tan \, \phi \, = \, -\dfrac{3}{4}$
$As, \, P \, = \, \dfrac{V^2 _{rms}}{Z}$

$\Rightarrow \, Z \, = \, \dfrac{V^2 _{rms}}{P} \, = \, \dfrac{(223)^2}{2000} \, =  \dfrac{49729}{2000} \, = \, 24.86 \, \Omega \, or \, Z \, = \, 25 \, \Omega$

$\tan \, \phi \, = \, \dfrac{X _C \, - \, X _L}{R} \, = \, - \dfrac{3}{4} \, \therefore \, X _C \, - \, X _L \, = \, -\dfrac{3}{4} R.$

AS, $Z^2 \, = \, R^2 \, + \, (X _C \, - \, X _L)^2$
$\therefore \, (25)^2 \, = \, R^2 \, + \, \left(-\dfrac{3}{4} \, R \right)^2$
$625 \, = \, \dfrac{25 \, R^2}{16}.$
$R^2 \, = \, \dfrac{625 \, \times \, 16}{25} \,  \, \Rightarrow \, R \, = \, 20 \, \Omega$

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

A voltage of peak value 283 V and varying frequency is applied to series LCR combination in which R = 3$\Omega$, L = 25 mH and C = 400$\mu$F. Then the frequency (in Hz) of the source at which maximum power is dissipated in the above is

  1. 51.5

  2. 50.7

  3. 51.1

  4. 50.3
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Here, $V _0 \, = \, 283 \, V, \, R \, = \, 3\Omega, \, L \, = \, 25 \, \times \, 10^{-3} \, H$
$C \, = \, 400 \, \mu F \, = \, 4 \, \times \, 10^{-4} F$
Maximum power is dissipated at resonance, for which 

$\nu \, = \, \dfrac{1}{2\pi \sqrt{LC}} \, = \, \dfrac{1 \, \times \, 7}{2 \, \times \, 22 \, \sqrt{25 \, \times \, 10^{-3} \, \times \, 4 \, \times \, 10^{-4}}}$

$= \, \dfrac{7 \, \times \, 10^3}{44\sqrt{10}} \, = \, 50.3 \, Hz$

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

A coil has a resistance $ 10 \Omega $ and an inductance of 0.4 henry. It is connected to an AC source of $ 6.5 V , \frac {30} { \pi } Hz. $ The average power consumed in the circuit, is :

  1. $ \cfrac {5} { 8} W $

  2. $ \cfrac {4} {3} W $

  3. $ \cfrac {3} {8} W $

  4. $ \cfrac {6} {7} W $
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The impedance Z = sqrt(R^2 + XL^2). XL = 2 * pi * f * L = 2 * pi * (30/pi) * 0.4 = 24 ohms. Z = sqrt(10^2 + 24^2) = sqrt(100 + 576) = 26 ohms. Current I = V/Z = 6.5 / 26 = 0.25 A. Power P = I^2 * R = (0.25)^2 * 10 = 0.0625 * 10 = 0.625 W, which is 5/8 W.

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

The power loss in an $AC$ circuit is $E _{rms}$ $I _{rms}$, when in the circuit there is only

  1. $C$

  2. $L$

  3. $R$

  4. $L,\ C$ and $R$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Inductors and capacitors bring a phase difference between the voltage and current in the circuit, hence changing the p.f. When only a resistance is present, $Poer\ factor= 1$.
The power loss in an AC circuit$ =E _{rms} I _{rms} Power\ factor $

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

The self inductance of the motor of an electric fan is 10 H. In order to impart maximum powr of 50 Hz, it should be connected to a capacitance of

  1. $8\mu F$

  2. $4\mu F$

  3. $2\mu F$

  4. $1\mu F$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Maximum power ($ I^2 R )$ is obtained when $I$ is maximum ( $Z$ is minimum).

For $Z$ minimum, $X _L=X _C$, which yields
$C=\dfrac {1}{(2\pi n)^2L}=\dfrac {1}{4\pi^2\times 50\times 50\times 10}$

$\therefore C=0.1\times 10^{-5}F=1\ \mu F$

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

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