RLC Circuit

Q.

Four charges q, 2q, 3q and 4q are placed at corners A, B, C and D of a square as shown in the figure below. Find the direction of electric field at the centre P of the square.

Q. 15.Two capacitor rated 600 pF, 4 kV and 300 pF , 6 kV can work in series up to the potential of ??

Q. A light bulb, a capacitor and a battery are connected together as shown here, with switch $S$ initially open. When the switch $S$ is closed, which one of the following is true ?

1. The bulb will light up for an instant when the capacitor starts charging.
2. The bulb will light up when the capacitor is fully charged.
3. The bulb will not light up at all.
4. The bulb will light up and go off at regular intervals.

Q. In the circuit shown in figure neglecting source resistance, the voltmeter and ammeter readings will respectively be

1. $0\text{V},8\text{A}$
2. $0\text{V},3\text{A}$
3. $150\text{V},6\text{A}$
4. $150\text{V},3\text{A}$

Q.

In the network shown below, points A, B and C are at the potential of 70 V, 0 V and 10 V respectively. The potential of point D is

1. 10 V

2. 20 V

3. 40 V

4. 30 V

Q. A parallel plate capacitor with the plate area $100{\text{cm}}^2$ and the separation between the plates $1.0\text{cm}$ is connected across a battery of emf $24\text{V}$. Find the force of attraction between the plates.

1. $2.55\times {10}^{-7}\text{N}$
2. $5\times {10}^{-7}\text{N}$
3. $7.25\times {10}^{-7}\text{N}$
4. $9.11\times {10}^{-7}\text{N}$

Q. How will the reading of ammeter change if the key $k$ is closed?

1. Increases
2. Decreases
3. Remains same
4. Information is insufficient

Q. A $20$ Henry inductor coil is connected to a $10$ ohm resistance in series as shown in figure. The time at which rate of dissipation of energy (joule's heat) across resistance is equal to the rate at which magnetic energy is stored in the inductor is

1. $\ln 2$
2. $\frac{1}{2}\ln 2$
3. $2\ln 2$
4. $\frac{2}{\ln 2}$

Q. In the given circuit, if point $C$ is connected to the earth and a potential of $2000\text{V}$ is given to point $A$. The potential at $B$ is

1. $1500\text{V}$
2. $500\text{V}$
3. $400\text{V}$
4. $1000\text{V}$

Q. An arc lamp requires a direct current of $10A$ at $80V$ to function. If it is connected to a $220V$ (rms), $50Hz$ AC supply, the series inductor needed for it to work is close to

1. $80H$
2. $0.08H$
3. $0.044H$
4. $0.065H$

Q. An electron beam has an aperture $1.0{\text{mm}}^2$. A total of $6.0\times {10}^{16}$ electrons go through any perpendicular cross-section per second. Find $\left(a\right)$ the current and $\left(b\right)$ the current density in the beam.

1. $9.6\times {10}^{-3}\text{A}\&9.6\times {10}^3{\text{A/m}}^2$
2. $9.6\times {10}^3\text{A}\&9.6\times {10}^{-3}{\text{A/m}}^2$
3. $6.3\times {10}^{-3}\text{A}\&6.3\times {10}^3{\text{A/m}}^2$
4. $3.2\times {10}^{-3}\text{A}\&3.2\times {10}^3{\text{A/m}}^2$

Q. An inductive coil has a resistance of $100\Omega$. When an A.C. signal of frequency $1000\text{Hz}$ is fed to the coil, the applied voltage leads the current by ${45}^{\circ }$. What is the approximate inductance of the coil (in $\text{mH}$) ?

Q. When an inductor, a capacitor and a resistor are connected in series across a source of alterating emf, the potential difference across the inductor, capacitor and resistor are 70V, 30V and 30V respectively. Find the emf of the source

1. 50V
2. 60V
3. 30V
4. 80V

Q. One 10 V, 60 W bulb is to be connected to 100 V line. The required induction coil has self inductance of value (f = 50 Hz)

1. 0.052 H
2. 2.42 H
3. 1.62 mH
4. 16.2 mH

Q. A charged 30 μF capacitor is connected to a 27 mH inductor. What isthe angular frequency of free oscillations of the circuit?

Q. The effective spring constant of the system in the figure shown is,

1. 
2. 
3. 
4. 

Q. The inductance of a solenoid is $5\text{H}$ and its resistance is $5\Omega$. If it is connected to a $10\text{Volt}$ battery, then time taken by the current to reach ${\frac{9}{10}}^{th}$ of its maximum will be

1. $4.0\text{s}$
2. $2.3\text{s}$
3. $1.4\text{s}$
4. $1.2\text{s}$

Q. In the given circuit, an ideal voltmeter connected across the $10\Omega$ resistance reads $2V$ . The internal resistance $r$, of each cell is

1. $1.5\Omega$
2. $0.5\Omega$
3. $1\Omega$
   
4. $0\Omega$

Q. A resistor R, an inductor L and a capacitor C are connected in series to an oscillator of frequency n. If the resonant frequency is , then the current lags behind voltage, when

1. n < n_r
2. n = n_r
3. n > n_r
4. n = 0

Q. A 420 V dc shunt motor takes 6 A at no - load. Its armature resistance (including brushes) is $1\Omega$ and shurt field resistance is $210\text{ohm}$. The effciencey when motor takes 52 A on full load is____%

1. 78.71

Q.

When two capacitors C₁ and C₂ are connected in series and parallel, their equivalent capacitances comes out to be 3 μF and 16 μFrespectively. Calculate values of C₁ and C₂.

1. 6 μF and 10 μF

2. 4 μF and 12 μF

3. 4 μF and 10 μF

4. 6 μF and 12 μF

Q. For an LCR series circuit with an ac source of angular frequency $\omega$,

1. Circuit will be capacitive if $\omega >\frac{1}{\sqrt{LC}}$
2. Circuit will be capacitive if $\omega =\frac{1}{\sqrt{LC}}$
3. Power factor of circuit will be unity if capacitive reactance equals inductive reactance
4. Circuit will be leading voltage if $\omega >\frac{1}{\sqrt{LC}}$

Q. Which of the following options represents correct dimensions of ${ϵ}_o$?

1. $\left[M^{-1}{L}^{-3}{T}^4{A}^2\right]$
2. $\left[M^0{L}^{-3}{T}^3{A}^3\right]$
3. $\left[M^{-1}{L}^{-3}{T}^{3}A\right]$
4. $\left[M^{-1}{L}^{-3}T{A}^2\right]$

Q. A series LCR circuit containing a resistor of $120\Omega$ has an angular resonant frequency $4\times {10}^{5}rad{s}^{-1}$. At resonance the voltages across resistor and inductor are 60 V and $40\text{V}$ respectively.
The value of capacitance C is

1. $\frac{1}{32}\mu F$
2. $\frac{1}{16}\mu F$
3. $32\mu F$
4. $16\mu F$

Q. The equivalent resistance between $A$ and $B$ is :

1. $\frac{7}{5}\Omega$
2. $\frac{13}{5}\Omega$
3. $\frac{16}{5}\Omega$
4. $2\Omega$

Q. In the given circuit, let $i_1$ be the current drawn from battery at time $t=0$ i.e. when switch is just closed and $i_2$ be steady state current at $t=\infty$, then the ratio $\frac{i_1}{i_2}$ is

Q. In a series LCR circuit the frequency of a 10V, AC voltage source is adjusted in such a fashion that the reactanace of the inductor measures 15 $\Omega$ and that of the capacitor 11$\Omega$, . If R = 3 $\Omega$ the potential difference across the series combination of L and C will be:

1. 8 V
2. 22 V
3. 10 V
4. 52 V

Q. When a voltage measuring device is connected to AC mains, the meter shows the steady input voltage of 220 V.
This means:

1. the meter reads not $v$ but $v^2$ and is calibrated to read $\sqrt{v^2}$
2. maximum input voltage is 220 V.
3. input voltage cannot be AC voltage, but a DC voltage.
4. the pointer of the meter is stuck by some mechanical defect.

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

1. $51.6$
2. $50.7$
3. $51.1$
4. $50.3$

Q. The diagram shows four capacitors with capacitance and break down voltages as mentioned. What should be the maximum value of the external emf source (in $kV$) such that no capacitor breaks down?