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Physics 1 Marks Question

Alternating Current · Bihar Board (BSEB) STD 12 Science (BSEB - English Medium). 43 questions.

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Question 11 Mark
A 60 µF capacitor is connected to a 110V, 60 Hz ac supply. Determine the rms value of the current in the circuit.
Answer
Given : $C=60 \mu F=60 \times 10^{-6} F$
$E _{ rms }=110 V$
$f=60 Hz$
$I _{ rms }=?$
$I_{r m s}=\frac{E_{r m s}}{X_C}=\omega C E_{r m s} \quad\left(\because X_C=\frac{1}{\omega C}\right)$
$\therefore \quad I _{ rms }=2 \pi f C E _{ rms }$
$=2 \times 3.14 \times 60 \times 60 \times 10^{-6} \times 110$
$=2.49 A$
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Question 21 Mark
A 100 Ω resistor is connected to a 220 V, 50 Hz supply.
(a) What is the rms value of the current?
(b) What is the net power consumed over a full cycle?
Answer
Given : $\quad R =100 \Omega$
$E _{ rms }=220 V$
$f=50 Hz$
(a)$I_{rms}=\frac{E_{rms}}{R}$
$=\frac{220}{100}=2.2 A$
(b)$P=I_{rms} \times E_{rms}$
$\begin{array}{l}=2.2 \times 220 \\
=484 W \text { per cycle. }\end{array}$
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Question 31 Mark
The instantaneous magnitudes of current and voltage in an ac circuit are given as $I =10 \sin 314 t A$ and $V =50 \sin \left(314 t +\frac{\pi}{2}\right) \quad V$ respectively. What is the dissipation of average power in the circuit?
Answer
Phase difference between voltage and current $=\frac{\pi}{2}$
$\therefore \quad \cos \phi=\cos \frac{\pi}{2}=0$
$\therefore \quad$ Average power $\quad \begin{aligned}
\overline{\mathrm{P}}  =\mathrm{V}_{\mathrm{rms}} \mathrm{I}_{\mathrm{rms}} \cos \phi \\  =\mathrm{V}_{\mathrm{rms}} \times \mathrm{I}_{\mathrm{rms}} \times 0=0\end{aligned}$
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Question 41 Mark
What is the principle on which a transformer works? Can it be used in de circuit?
Answer
It works on the principle of electromagnetic induction. It cannot work in de circuit because direct current cannot produce variable magnetic field in core of the transformer.
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Question 51 Mark
Power factor of an ac circuit is 0.5. What is the phase difference between current and voltage in the circuit?
Answer
$\cos \phi=0.5=\frac{1}{2}=\cos 60^{\circ}=\cos \frac{\pi}{3}$
Phase difference is $\frac{\pi}{3}$ radian.
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Question 61 Mark
In an ac circuit, instantaneous current and voltage are $I = I _0 \sin 300 t A$ and $V =200 \sin 300 t$ respectively. What is average power dissipated in the circuit?
Answer
It is clear from the given expressions that phase difference $\phi$ between current and voltage is $\phi=0^{\circ}$.
$\overline{ P }= V _{ rms } \cdot I _{ rms } \cos \phi$
$=\frac{V_0}{\sqrt{2}} \times \frac{I_0}{\sqrt{2}} \times \cos 0^{\circ}$
$=\frac{200}{\sqrt{2}} \times \frac{10}{\sqrt{2}} \times 1$
$=1000 W$
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Question 71 Mark
Expression $E = E _0 \sin \omega t$ represents alternating electromotive force. Find its frequency, magnitude and time period.
Answer
Angular frequency $\omega=2 \pi f,(f)=\frac{\omega}{2 \pi}$
Magnitude $=$ Peak value of voltage $= E _0$
Time period, $T =\frac{1}{f}=\frac{2 \pi}{\omega}$
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Question 81 Mark
Write the magnitude of average value of alternating current for a complete cycle.
Answer
The average value of alternating current for a complete cycle is zero.
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Question 91 Mark
Applied voltage in any ac circuit is 220 V . If $R =8 \Omega, X _{ L }= X _{ C }=6 \Omega$, then find the value of the following :(a) root mean square value of the voltage,
(b) impedance of the circuit.
Answer
(a) $ V_{rms}=220 V $
(b) Impedance of circuit $\quad Z =\sqrt{ R ^2+\left( X _{ L }- X _{ C }\right)^2}$
Now, $X_L=X_C$ then $Z=R$
Impedance of circuit $Z=8 \Omega$.
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Question 101 Mark
Write the definition of root mean square value of alternating current.
Answer
The square root of the mean square of the instantaneous value of alternating curent is called the root mean square value $I_{ rms }$ of the current.
$I ^2= I _0^2 \sin ^2 \omega t$
$I _{ rms }=\frac{ I _0}{\sqrt{2}}$ or $I _{ rms }=0.707 I _0$
Root mean square value of ac current is obtained by multiplying its peak value by $\frac{1}{\sqrt{2}}$ or 0.707
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Question 111 Mark
When an electrical component $X$ is joined with any ac circuit, then current in it is ahead of phase of voltage by $\frac{\pi}{2}$ radian. Identify X and write an expression for its reactance.
Answer
Component X is a capacitor and its reactance $ =\frac{1}{\omega C}=\frac{1}{2 \pi / C} $
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Question 121 Mark
If an ac circuit, $R=100 \Omega, X_L=400 \Omega$ and $X _{ C }=400 \Omega$, then what is the total impedance of the circuit?
Answer
Impedance $Z=\left( R ^2+\left( X _{ L }- X _{ C }\right)^2\right)^{1 / 2}$
When $X_L=X_C $
then $Z =\left( R ^2+0\right)^{1 / 2}= R$
$\therefore \quad Z=100 \Omega$
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Question 131 Mark
Is it possible in a LCR series circuit that the value of applied potential on any component of circuit is more than the peak value of applied alternating potential?
Answer
Yes, in a capcitor or inductor.
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Question 141 Mark
Which is more dangerous ac current or de current of same voltage?
Answer
Alternating current because the peak value of potential in ac is more than in dc.
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Question 151 Mark
An inductor and a resistor are joined in series with any ac source. What is the phase difference in the potential difference across their ends?
Answer
$\frac{\pi}{2}$ radian.
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Question 161 Mark
Can alternating current cause electrolysis?
Answer
No, because alternating current changes periodically whereas for the process of electrolysis, the magnitude nad direction of current does not change with time.
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Question 171 Mark
Can a battery be charged with alternating current?
Answer
No, because direction of ac current changes periodically.
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Question 181 Mark
Show by a graph, how inductive reactance varies with frequency of alternating source?
Answer
$X _{ L }=\omega L$
$X_L \propto \omega$
Image
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Question 191 Mark
What is the average power given by an ac source to a capacitor?
Answer
Phase difference between voltage and current in a capacitor $=\phi=90^{\circ}$
Average power $\overline{ P }= E _{ mxx } I _{ rms } \cos \phi=0$$\because \cos 90^{\circ}=0$
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Question 201 Mark
Can alternating galvanometer measure both alternating and direct currents?
Answer
Yes, because it works on principle of heating effect.
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Question 211 Mark
If in any electric circuit, phase of current lags the phase of potential difference by 90°, then what is the nature of reactance of the circuit?
Answer
Inductive
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Question 221 Mark
What is the value of inductive reactance in. pure inductor de circuit?
Answer
Zero, because $X_L=\omega L$ and in direct current $\omega=0$.
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Question 241 Mark
What is the relation between peak value and root mean square value of alternating voltage?
Answer
$E _{ rms }=\frac{ E _0}{\sqrt{2}}$,
where $E_0$ is peak value of alternating voltage.
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Question 251 Mark
An ac current $I = I _0 \sin \omega t$ produces some heat H in any resistor R in time $T =\frac{2 \pi}{\omega}$. Write the magnitude of dc current which will produce same heat in same resistor in same time.
Answer
Required dc current $=$root mean square value of alternating current
$ I_{rms}=\frac{I_0}{\sqrt{2}} $
where $I_0$ is peak value of alternating current.
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Question 261 Mark
A resistor, inductor and a capacitor are joined with a de source. What is the magnitude of impedance of the circuit?
Answer
Infinite because in dc, $\omega=0$
$ \therefore \text { Impedance }=\sqrt{R^2+\left(\omega L-\frac{1}{\omega C}\right)^2}$
$\therefore Z=\infty$
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Question 271 Mark
When a transformer is known as an ideal transformer?
Answer
In an ideal transformer, there is no loss in energy on transferring the energy from primary coil to secondary coil and then the value of power is same in both the coils. Efficiency of such transformer should be $100 \%$.
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Question 281 Mark
What is the power factor of pure inductor or capacitor?
Answer
Zero as phase angle in inductor or capacitor $=$$\pm \frac{\pi}{2} \text {. }$
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Question 291 Mark
How will you determine that current flowing through the filament of a bulb is ac or dc?
Answer
On bringing magnet near it, if there is vibration in the filament then current is ac.
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Question 301 Mark
Calculate power loss in an ac circuit in which magnitudes of voltage and current are as follows :$V =3000 \sin \left(\omega t+\frac{\pi}{2}\right)$ and $I =5 \sin \omega t$
Answer
Here $\phi=\frac{\pi}{2}$
$P = E _{ rms } I _{ rms } \cos \phi$
$\therefore \quad P=0$ $\because \cos \frac{\pi}{2}=0$
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Question 311 Mark
If primary coil of a transformer is joined with a battery, then what will happen?
Answer
For a current will flow in the secondary coil for an instant and then no current will flow.
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Question 321 Mark
What is the function of step up transformer?
Answer
To change high current of low voltage into low current of high voltage.
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Question 331 Mark
Which quantity remain constant in a transformer? Current, potential, frequency or power?
Answer
Frequency
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Question 341 Mark
State any two factors responsible for energy loss in practical transformer.
Answer
(i) Flux loss, (ii) Eddy current loss
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Question 351 Mark
Write phase difference between applied emf and current in pure resistor, inductor and capacitor.
Answer
Phase difference $\phi=0$ current lags by $\frac{\pi}{2}$, voltage lags by $\frac{\pi}{2}$.
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Question 361 Mark
Electric lines in households works at 220 V. What is the magnitude of peak value of emf?
Answer
We know that
$E_{ rms }=\frac{ E _0}{\sqrt{2}}$ $\therefore E _0=\sqrt{2} E _{ rms }$
$E _0=1.414 \times 220$
$=310.2$ volt Ans.
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Question 371 Mark
A capacitor and a bulb are joined in series with an ac voltage source. If frequency of alternating emf is increased then what is the effect on the circuit?
Answer
On increasing the frequency, reactance of capacitor $\frac{1}{ C \omega}$ decreases due to which current in the circuit increases and brightness of bulb increases.
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Question 381 Mark
What is the meaning of instantaneous power and average power in an ac circuit?
Answer
The magnitude of power at any instant in an ac circuit is known as instantaneous power and average value of instantaneous powers in one complete cycle is known as average power.
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Question 391 Mark
Two bulbs of 25 W and 50 W are joined in series. Which will give more light and why?
Answer
In 25 W bulb. Same current will flow through both of them. Due to greater resistance of 25 W bulb, more heat will be produced in it.
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Question 401 Mark
If peak value of alternating current is Io, then what is the magnitude of (a) rms value of current and (b) average value of current?
Answer
(a) Root mean square value of current
$ I_{\operatorname{rass}}=\frac{I_0}{\sqrt{2}} $
(ii) Magnitude of average current, $\overline{ I }=0$
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Question 411 Mark
Resistance of a coil is 30 and its reactance is 42. What is power factor of the coil?
Answer
Power factor $=\frac{R}{Z}$
But $Z =\sqrt{( R )^2+\text { Reactance }^2}$
$=\sqrt{(3)^2+(4)^2}=5$
$\therefore \quad$ Power factor $=\frac{R}{Z}=\frac{3}{5}$ Ans.
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Question 431 Mark
Voltage across the ends of inductor, capacitor and resistor in a series LCR circuit is 20 V, 20 V and 40 V respectively. What is the phase difeerence between the current and applied voltage in the circuit?
Answer
$\tan \phi=\left(\frac{ V _{ C }- V _{ L }}{ V }\right)=\left(\frac{20-20}{40}\right)=0$
$\phi=\tan ^{-1}(0)=0$
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