Alternating Current

Q.

The dielectric strength of air is $3.0\times {\underset{2}{10}}^6$ V/m. A parallel-plate air-capacitor has area 20 $c{m}^2$ and plate separation 0.10 mm. Find the maximum rms voltage of an AC source which can be safely connected to this capacitor.

Q. An infinitely long straight wire carrying current $I$, one side opened rectangular loop and a conductor $C$ with a sliding connector are located in the same plane, as shown in the figure. The connector has length $l$ and resistance $R$. It slides to the right with a velocity $v$. The resistance of the conductor and the self inductance of the loop are negligible. The induced current in the loop, as a function of separation $r$, between the connector and the straight wire is

1. $\frac{{\mu }_0}{4\pi }\frac{Ivl}{Rr}$
2. $\frac{{\mu }_0}{\pi }\frac{Ivl}{Rr}$
3. $\frac{2{\mu }_0}{\pi }\frac{Ivl}{Rr}$
4. $\frac{{\mu }_0}{2\pi }\frac{Ivl}{Rr}$

Q.

How does an inductor behave in DC?

Q. The current flowing through an $ac$ circuit is given by $I=5sin\left(120\pi t\right)\text{A}$. How long will the current take to reach the peak value at the earliest starting from zero?

1. $60\text{s}$
2. $\frac{1}{120}\text{s}$
3. $\frac{1}{60}\text{s}$
4. $\frac{1}{240}\text{s}$

Q. A coil of 0.01 henry inductance and 1 ohm resistance is connected to 200 Volt, 50 Hz AC supply.
1) Find the impedance of the circuit.
2) Find the time lag between max. alternating voltage and current.

Q. In a region of uniform magnetic induction $B={10}^{-2}tesla$, a circular loop of radius 30 cm and resistance ${\pi }^2$ ohm is rotated about an axis which is perpendicular to the direction of B and which forms a diameter of the loop. If the loop rotates at 200 rpm , the maximum amplitude of the alternating current induced in the loop is

1. $4{\pi }^{2}mA$
2. 30 mA
3. 6 mA
4. 200 mA

Q. The charge on a parallel plate capacitor varies as $q=q_0\cos 2\pi vt$.
The plates are very large and close together (area = A, separation = d).

Neglecting the edge effects, find the displacementcurrent through the capacitor?

Q. If $q=q_0(1-e^{\frac{t}{RC}})$, here,
$q=$ electric charge, $R=$ electric resistance,
$C=$ electric capacitance. The dimensional formula for is

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

Q.

Which is more Powerful AC or DC?

Q. The thermo e.m.f. $E$ in volts of a certain thermo-couple is found to vary with temperature difference $\theta$ in ${}^{\circ }C$ between the two junctions according to the relation
$E=30\theta -\frac{{\theta }^2}{15}$. The neutral temperature for the thermo-couple will be

1. ${225}^{\circ }\text{C}$
2. ${450}^{\circ }\text{C}$
3. ${400}^{\circ }\text{C}$
4. ${30}^{\circ }\text{C}$

Q. The magnetic field $B$ shown in the figure is directed into the plane of the paper. $\text{ACDA}$ is a semicircular conducting loop of radius $r$ with the centre at $\text{O}$. The loop is now made to rotate clockwise with a constant angular velocity $\omega$ about an axis passing through $O$ and perpendicular to the plane of the paper. The resistance of the loop is $R$. Obtain an expression for the magnitude of the induced current in the loop.

1. $\frac{B\omega r^2}{4R}$
2. $\frac{B\omega r^2}{R}$
3. $\frac{B\omega r^2}{2R}$
4. $\frac{2B\omega r^2}{R}$

Q. If charge flowing through a conductor is given by $q=1.5t^2+t$. Then the current (in amperes) caused in $t=2s$ will be

Q.

Four resistors of $3\Omega$, $5\Omega$, $7\Omega$ and $10\Omega$ are connected in series to a $10V$ battery. Calculate the current in $5\Omega$ resistor.

Q. Loop $\text{A}$ of radius $r(<<R)$ moves towards loop $\text{B}$ with a constant velocity $v$ in such a way that their planes are always parallel. What is the distance between the two loops $\left(x\right)$ when the induced e.m.f in loop $\text{A}$ is maximum?

1. $R$
2. $\frac{R}{\sqrt{2}}$
3. $\frac{R}{2}$
4. $R(1-\frac{1}{\sqrt{2}})$

Q. Explain the energy losses in a transformer. How are they minimized?

Q. In a circuit shown, voltmeter reads $3V$ and the ammeter reads $2A$. The emf $E$ (in $Volt$) is

Q. Study the circuits (a) and (b) shown in figure and answer the following question.

i) Under which conditions would the rms currents in the two circuits be the same?
ii) Can the rms current in circuit (b) be larger than
that in (a)?

Q.

A cell of $e.m.f.1.8V$ is connected to an external resistance of $2\Omega$, when$p.d$. recorded at the ends of resistance is $1.6\text{volts}$. Calculate the internal resistance of the cell.

Q. For the configuration of capacitors shown, both switches are closed simultaneously. After equilibrium is established, what is charge on the top plate of the $5\mu F$ capacitor?

1. $10\mu C$
2. $90\mu C$
3. $100\mu C$
4. None of these

Q. In a series resonant circuit, the ac voltage across resistance $R$, inductance $L$ and capacitance $C$ are $5V,10V$ and $10V$ respectively. The ac voltage applied to the circuit will be

1. $20V$
2. $10V$
3. $5V$
4. $25V$

Q. A coil $\text{A}$ of radius $R$ and number of turns $n$ carries a current $i$ and it is placed in a horizontal plane. A small conducting ring $\text{P}$ of radius $r(r<<R)$ is placed at a height $y$ above the centre of the coil $\text{A}$ as shown in the figure. Calculate the induced $\text{emf}$ in the ring when the ring is allowed to fall freely. Express the induced $\text{emf}$ as a function of instantaneous speed $v$ of the falling ring and its height $y$ above the centre of the coil $\text{A}.$

1. $\frac{3}{2}\frac{{\mu }_0\pi ni{R}^2{r}^{2}yv}{(R^2+y^2{)}^{3/2}}$
2. $\frac{3}{2}\frac{{\mu }_0\pi ni{R}^2{r}^{2}yv}{(R^2+y^2{)}^{5/2}}$
3. $\frac{1}{2}\frac{{\mu }_0\pi ni{R}^2{r}^{2}yv}{(R^2+y^2{)}^{5/2}}$
4. $\frac{2{\mu }_0\pi ni{R}^2{r}^{2}yv}{(R^2+y^2{)}^{5/2}}$

Q. how to find rms and peak voltage values ?

Q. How can a galvanometer be converted into an ammeter?

Q.

Which is not true for three-phase AC?

1. The three-phase power supply has three distinct wave cycles.

2. The voltage of three-phase is 230 V.

3. The efficiency of three-phase is high compared to single-phase

4. Three-phase is expensive compared to single-phase

Q.

The phase difference between the input and output voltage of CE amplifier circuit is

1. 180⁰

2. 90⁰

3. 270⁰

4. 0⁰

Q. What is a transistor? Why is it so called? What are the advantages of transistors over vacuum tubes?

Q. Two coaxial circular loops of radii $0.5\text{m}$ and $0.05\text{m}$ are separated by a distance of $0.5\text{m}.$ The current in the coil of radius $0.5\text{m}$ varies as $i=\left(2t\right)\text{A}.$ If the emf induced in the small coil is $e$ and the mutual inductance between the coils is $M,$ then which of the following is correct-

$\left(i\right).M=2.5\times {10}^{-9}\text{H}$

$\left(ii\right).e=2.5\times {10}^{-9}\text{V}$

$\left(iii\right).M=5\times {10}^{-9}\text{H}$

$\left(iv\right).e=5\times {10}^{-9}\text{V}$

1. $\left(i\right)$ and $\left(ii\right)$
2. $\left(ii\right)$ and $\left(iii\right)$
3. $\left(i\right)$ and $\left(iv\right)$
4. $\left(ii\right)$ and $\left(iv\right)$

Q. A galvanometer can be converted into a voltmeter by connecting :

1. Low resistance in parallel
2. Low resistance in series
3. High resistance in parallel
4. High resistance in series

Q.

Answer the following questions:

(a) In any ac circuit, is the applied instantaneous voltage equal to the algebraic sum of the instantaneous voltages across the series elements of the circuit? Is the same true for rms voltage?

(b) A capacitor is used in the primary circuit of an induction coil.

(c) An applied voltage signal consists of a superposition of a dc voltage and an ac voltage of high frequency. The circuit consists of an inductor and a capacitor in series. Show that the dc signal will appear across C and the ac signal across L.

(d) A choke coil in series with a lamp is connected to a dc line. The lamp is seen to shine brightly. Insertion of an iron core in the choke causes no change in the lamp’s brightness. Predict the corresponding observations if the connection is to an ac line.

(e) Why is choke coil needed in the use of fluorescent tubes with ac mains? Why can we not use an ordinary resistor instead of the choke coil?

Q.

The phase difference between input and output voltages of a CE circuit is

1. 90^o

2. 0^o

3. 180^o

4. 270^o