Download App

Alternating Current — Physics STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 SciencePhysicsAlternating Current5 Marks
Question
  1. Derive an expression for the average power consumed in a series LCR circuit connected to a.c. source in which the phase difference between the voltage and the current in the circuit is $\phi$.
  2. Define the quality factor in an a.c. circuit. Why should the quality factor have high value in receiving circuits? Name the factors on which it depends.
✓

Answer

  1. In a series LCR circuit.
Voltage $\text{v} = \text{v}_{m} \sin\omega\text{t}$
Current in the circuit is given by $\text{i} =\text{i}_{m} \sin\big(\omega\text{t} + \Phi\big)$
Therefore, the instantaneous power $p_i$ supplied by the source is $\text{p}_{i} = \text{vi} = \big(\text{V}_{m}\sin\omega\text{t}\big)\times[\text{i}_{m}\sin\big(\omega\text{t} + \phi\big)]$

$ =\frac{\text{v}_{m}\text{i}_{m}}{2}[cos\phi - cos\big(2\omega\text{t} +\phi\big)]$
The average power over a cycle is given by the average of the two terms on the R.H.S.. It is only the second term which is time-dependent. Its average over a complete cycle is zero (the positive half of the cosine cancels the negative.
$\text{P}_{av}$
$ = \text{VI} \cos \phi$
  1. Quality factor: The ratio of the voltage drop (in a series LCR circuit) across the inductor (or capacitor) to the voltage drop across resistor under resonance conditions.
Reason: Selectivity (or sharpness of resonance) of the circuit becomes large.
Factors: depends on inductance , capacitance and resistance.

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "5 Marks Questions" from Alternating Current→Alternating Current — all question types→Physics STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

Let $\text{X}=\overline{\text{ABC}}+\overline{\text{BCA}}+\overline{\text{CAB}}.$ Evaluate X for:
  1. $\text{A}=1,\text{B}=0,\text{C}=1$
  2. $\text{A}=\text{B}=\text{C}=1$
  3. $\text{A}=\text{B}=\text{C}=0$
→
In an agricultural experiment, a solution containing 1 mole of a radioactive material $\Big(\text{t}_{\frac{1}{2}}=14.3\text{ days}\Big)$ was injected into the roots of a plant. The plant was allowed 70 hours to settle down and then activity was measured in its fruit. If the activity measured was $1\mu\text{Ci},$ what per cent of activity is transmitted from the root to the fruit in steady state?
→
$i.$ An ac source generating a voltage $V = V _0 \sin \omega t$ is connected to a capacitor of capacitance $C$ . Find the expression of the current I flowing through it. Plot a graph of $V$ and $I$ versus $\omega t$ to show that the current is $\frac{\pi}{2}$ ahead of the voltage.
$ii.$ A resistor of $200 \Omega$ and a capacitor of $15 \mu F$ are connected in series to a $220 V, 50 \ Hz$ ac source. Calculate the current in the circuit and the rms voltage across the resistor and the capacitor. Why the algebraic sum of these voltages is more than the source voltage?
→
How many wavelengths are emitted by atomic hydrogen in visible range (380nm-780nm)? In the range 50nm to 100nm?
→
  1. Draw a schematic sketch of a cyclotron. Explain clearly the role of crossed electric and magnetic field in accelerating the charge. Hence derive the expression for the kinetic energy acquired by the particles.
  2. An α–particle and a proton are released from the centre of the cyclotron and made to accelerate.
    1. Can both be accelerated at the same cyclotron frequency? Give reason to justify your answer.
    2. When they are accelerated in turn, which of the two will have higher velocity at the exit slit of the dees?
→
A piston is fitted in a cylindrical tube of small cross-section with the other end of the tube open. The tube resonates with a tuning fork of frequency 512Hz. The piston is gradually pulled out of the tube and it is found that a second resonance occurs when the piston is pulled out through a distance of 32.0cm. Calculate the speed of sound in the air of the tube.
→
Use (i) the Ampere's law for H and (ii) continuity of lines of B, to conclude that inside a bar magnet, (a) lines of H run from the N pole to S pole, while (b) lines of B must run from the S pole to N pole.
→
The Bohr model for the H-atom relies on the Coulomb’s law of electrostatics. Coulomb’s law has not directly been verified for very short distances of the order of angstroms. Supposing Coulomb’s law between two opposite charge $+q_1, -q_2$ is modified to
$|\text{F}|=\frac{\text{q}_1\text{q}_2}{(4\pi\in_0)}\frac{1}{\text{r}^2}.\text{r}\geq\text{R}_0$
$=\frac{\text{q}_1\text{q}_2}{(4\pi\in_0)}\frac{1}{\text{R}^2_0}\Big(\frac{\text{R}_0}{\text{r}}\Big)^{\in}.\text{r}\geq\text{R}_0$
Calculate in such a case, the ground state energy of a H-atom, if $\in=0.1,\text{R}_0=1\mathring{\text{A}}$.
→
A voltmeter coil has resistance $50.0\Omega$ and a resistor of $1.15\text{k}\Omega$ is connected in series. It can read potential differences up to 12 volts. If this same coil is used to construct an ammeter that can measure currents up to 2.0A, what should be the resistance of the shunt used?
→
When an electron goes from the valence band to the conduction band in silicon, its energy is increased by 1.1eV. The average energy exchanged in a thermal collision is of the order of kT which is only 0.026eV at room temperature. How is a thermal collision able to take some of the electrons from the valence band to the conduction band?
→