Tag: physics

Questions Related to physics

In an a.c. circuit consisting of resistance $R$ and inductance $L$, the voltage across $R$ is $60$ volt and that across $L $ is $80$ Volt.The total Voltage across the combination is 

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

  1. $140 V$

  2. $20 V$

  3. $100 V$

  4. $70 V$

Show answer
Correct Option: C

Find the resonant frequency and $Q-factor$ of a series $LCR$ circuit with $L = 3.0\ H, C = 27\mu F$ and $R = 7.4\Omega$.

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

  1. $111\ rad/s, 45$

  2. $111\ rad/s, 90$

  3. $55.5\ rad/s, 45$

  4. $55.5\ rad/s, 90$

Show answer
Correct Option: A

The self inductance of a choke coil is mH. when it is connected with a 10 VDC source then the loss of power is 20 watt. When it connected with 10 volt AC source loss of power is 10 watt. The frequency of AC source will bw-

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

  1. 50 Hz

  2. 60 Hz

  3. 80 Hz

  4. 100 Hz

Show answer
Correct Option: A
Explanation:

$\begin{array}{l} When\, \, \, dc\, \, is\, \, pass\, \, through\, \, the\, \, inductor\, \, no\, \, induv\tan  ce\, \, effect\, \, will\, \, be\, \, their\, \, only \ resis\tan  ce\, \, will\, \, be\, their\, \, resis\tan  ce\, \, of\, \, the\, \, inductor\, \, be\, \, R \ 20=\frac { { 100 } }{ R }  \ R=5\Omega  \ Xl=\omega \times 0.001 \ power\, \, =\frac { { { v^{ 2 } } } }{ z } \cos  \phi  \ Z=\sqrt { 25+{ \omega ^{ 2 } }\times { { 10 }^{ -6 } } }  \ \cos  \phi =\frac { R }{ Z } =\frac { 5 }{ Z }  \ 10=\frac { { 100 } }{ Z } \frac { 5 }{ Z } =\frac { { 500 } }{ { { Z^{ 2 } } } } =\frac { { 500 } }{ { 25 } } +{ \omega ^{ 2 } }\times { 10^{ -6 } } \ 25+{ \omega ^{ 2 } }\times { 10^{ -6 } }=50 \ { \omega ^{ 2 } }=25\times { 10^{ 6 } } \ \omega =5000 \end{array}$
$=50 Hz$
Hence, Option $A$ is correct answer.

For watt-less power in an $AC$ circuit the phase angle between the current and voltage is

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

  1. $0^o$

  2. $90^o$

  3. $45^o$

  4. Not possible

Show answer
Correct Option: B
Explanation:

Watt-less power in an AC circuit is basically power supposed to be generated by inductive and capacitive reactance and since they are not resistor they generate any heat , and these power wasted is called watt-less power and its phase angle is always $90^o$ as it has only capacitor and inductor.

For an $LCR$ series circuit with an A.C. source of angular frequency $\omega$, which statement is correct?

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

  1. Circuit will be capacitive if $\omega > \displaystyle\frac{1}{\sqrt{LC}}$

  2. Circuit will be capacitive if $\omega = \displaystyle\frac{1}{\sqrt{LC}}$

  3. Power factor of circuit will be unity if capacitive reactance equals inductive reactance

  4. Current will be leading voltage if $\omega > \displaystyle\frac{1}{\sqrt{LC}}$

Show answer
Correct Option: C
Explanation:

Circuit will be capacitive if , total reactance =$ X _L - X _C < 0$

$ \Rightarrow  X _C > X _L \Rightarrow  \frac{1}{C \omega} >  L \omega  \Rightarrow \omega < \frac{1}{ \sqrt{ L C }} $

Current will be leading the voltage if the circuit is capacitive , i.e., $ \omega   < \frac{1}{ \sqrt{ L C }} $

Power factor= $ \dfrac{ R } { Z } $   ; pf factor will be unity if $ R= Z \Rightarrow X _L=X _C $ , i.e., capacitive reactance is equal to inductive reactance.

A $50\space W$, $100\space V$ lamp is to be connected to an AC mains of $200\space V, \space 50\space Hz$. What capacitor is essential to be put in series with the lamp?

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

  1. $\displaystyle\frac{25}{\sqrt2}\mu F$

  2. $\displaystyle\frac{50}{\pi\sqrt3}\mu F$

  3. $\displaystyle\frac{50}{\sqrt2}\mu F$

  4. $\displaystyle\frac{100}{\pi\sqrt3}\mu F$

Show answer
Correct Option: B
Explanation:

for $100V, 50 W $lamp , $ R = \frac{100^2}{50} = 200 \Omega $
capacitor put in series should be such that, 
$ V _R = \frac{ R} { \sqrt{ R^2 + X _C^2 } } V _s= 100 $
$ \Rightarrow  \frac{1}{C \omega} =  X _C= \sqrt{3} R $
$ C=\frac{1}{ \omega \sqrt{3} R } =\frac{50}{\pi \sqrt{3} } \mu F $

In an A.C. circuit, the current flowing in inductance is $\displaystyle I=5\sin { \left( 100t-{ \pi  }/{ 2 } \right)  } $ ampers and the potential difference is V = 200 sin (100 t) volts. The power consumption is equal to 

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

  1. 1000 watt

  2. 40 watt

  3. 20 watt

  4. Zero

Show answer
Correct Option: D
Explanation:

Power, $\displaystyle P={ I } _{ r.m.s }\times { V } _{ r.m.s }\times \cos { \phi  } $
In the given problem, the phase difference between voltage and current is p/2. Hence
$\displaystyle P={ I } _{ r.m.s }\times { V } _{ r.m.s }\times \cos { \left( { \pi  }/{ 2 } \right)  } =0\ $

An inductor $20$ mH, a capacitor $100$ $\mu$F and a resistor $50$ $\Omega$ are connected in series across a source of emf, V$=10$ $\sin 314$t. The power loss in the circuit is?

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

  1. $2.74$ W

  2. $0.79$ W

  3. $1.13$ W

  4. $0.43$ W

Show answer
Correct Option: B
Explanation:

$L = 20 mH$ $C = 100 \mu F$ $R = 50 \Omega$

$V = 10 sin(314 t)$
$V _0= 10$, $\omega = 314$
$X _L = wL= 314 \times 20\times 10^{-3}= 6.28 \Omega$
$X _C = \dfrac{1}{\omega C}=31.8 \Omega$
$Z = \sqrt{R^2 + (X _C- X _L)^2} = 56.1 $
$Power \ loss P=\dfrac{V _0^2 R}{2 Z^2}= 0.79 W$


Assertion: A resistance is connected to an ac source. Now a capacitor is included in the series circuit. The average power absorbed by the resistance will remain same.  

Reason: By including a capacitor or an inductor in the circuit average power across resistor does not change.

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

  1. A and R both are true and R is correct explanation of A

  2. A and R both are true but R is not the correct explanation of A

  3. A is true R is false

  4. A is false and R is true

Show answer
Correct Option: D
Explanation:

After connecting the capacitor Irms will charge because impedance is changed.
$\therefore$ A is false

A reflecting telescope has a large mirror for its objective with radius of curvature equal to 80 cm. The magnifying power of this telescope if eye piece used has a focal length of 1.6 cm is:

physics option c: imaging optical instruments : telescope the reflecting telescope optical telescope xx radio telescope and space telescopes

  1. 100

  2. 50

  3. 25

  4. 5

Show answer
Correct Option: C
Explanation:

The focal length of objective mirror $f _0 = \dfrac{R}{2} = \dfrac{80}{2} = 40 \,cm$
and focal length of eye piece = 1.6 cm
$\therefore $ magnifying power, $m = \dfrac{f _0}{f _e} = \dfrac{40}{1.6 } = 25$