Mutual inductance - class-XII
| Description: mutual inductance | |
| Number of Questions: 94 | |
| Created by: Jayanti Mahajan | |
| Tags: physics electromagnetic induction and alternating currents electromagnetic induction |
The coefficient of mutual inductance between two coils depends on
Two coils of self inductances 2 mH and 8 mH are placed so close together that the effective flux in one coil is completely linked with the other. The mutual inductance between these coils is:
A circular copper disc 10 cm in diameter rotates at 1800 revolution per minute about an axis through its centre and at right angles to disc. A uniform field of induction B of 1 Wb $m^2$ is perpendicular to disc. What potential difference is developed between the axis of the disc and the rim ?
Mutual inductance of two coils can be increased by
If the self inductance of 500 turns coil is 125 mH, then the self inductance of the similar coil of 800 mH
The mutual inductance $M _{12}$ of a coil 1 with respect to coil 2
Match the following:
| Quantity | Formula |
|---|---|
| 1) Magnetic flux linked with a coil | a) $\displaystyle -N\frac { d\phi }{ dt } $ |
| 2) Induced emf | b) $\displaystyle { \mu } _{ r }{ \mu } _{ 0 }{ n } _{ 1 }{ n } _{ 2 }{ \pi r } _{ 1 }^{ 2 }l$ |
| 3) Force on a charged particle moving in a electric and magnetic field | c) $\displaystyle BA\cos { \theta } $ |
| 4) Mutual inductance of a solenoid | d) $\displaystyle q\left( \overline { E } +\overline { v } \times \overline { B } \right) $ |
In the method using the transformers, assume that the ratio of the number of turns in the primary to that in secondary in the step-up transformer is $1:10$. If the power to the consumer has to be supplied at $200\ V$, the ratio of the number of turns in the primary to that in the secondary in the step-down transformer is:
An inductor of inductance $100\ mH$ is connected in series with a resistance, a variable capacitance and an AC source of frequency $2.0\ kHz$; The value of the capacitance so that maximum current may be drawn into the circuit.
$5 \mathrm { mV }$ is induced in a coil, when current in another nearby coil changes by $5 \mathrm { A }$ in $0.1$sec. The mutual inductance between the two coils will be
In mutual induction
A: when current in one coil increases, induced current in neighbouring coil flows in the opposite direction
B: When current in one coil decreases, induced current in neighbouring coil flows in the opposite direction
In case of all flux from the current in coil 1 links with coil 2, the coefficient of coupling will be
The induction coil works on the principle of.
Two coils A and B have 200 and 400 turns respectively. A current of 1 A in coil A causes a flux per turn of $10^{-3}$ Wb to link with A and a flux per turn of $0.8 \times 10^{-3}$ Wb through B. The ratio of self-inductance of A and the mutual inductance of A and B is :
Two concentric coils each of radius equal to $2\pi\ cm$ are placed at right angles to each other. $3$ Ampere and $4$ ampere are the currents flowing in each coil respectively. The magnetic induction in $Weber/m^{2}$ at the centre of the coils will be ($\mu _{0}=4\pi \times 10^{-7}\ Wb/A-m$)
A 60 volt - 10 watt bulb is operated at 100 volt - 60 Hz a.c. The inductance required is?
Two coaxial coils are very close to each other and their mutual inductance is $5mH$. If a current $50sin{500t}$ is passed in one of the coils then the peak value of induced emf in the secondary coil will be
The coefficient of self induction of two inductor coils are $20mH$ and $40mH$ respectively. If the coils are connected in series so as to support each other and the resultant inductance is $80mH$ then the value of mutual inductance between the coils will be
For solenoid keeping the turn density constant its length makes halved and its cross section radius is doubled then the inductance of the solenoid increased by :
A rectangular loop of sides 'a' and 'b' is placed in the XY plane. A very long wire is also placed in xy plane such that side of length 'a' of the loop is parallel to the wire. The distance between the wire and the nearest edge of the loop is 'd'. The mutual inductance of this system is proportional to?
A circular loop of radius $r$ is placed at the centre of current carrying conducting square loop of side $a$. If both loops are coplanar and $a >> r$, then the mutual inductance between the loops will be:
A $50\ Hz$ $AC$ current of crest value $1\ A$ flows, through the primary of transformer. If the mutual inductance between the primary and secondary be $0.5\ H$, the crest voltage induced in the secondary is
Which of the following statement is correct?
An electron originates at a point $A$ lying on the axis of a straight solenoid and moves with velocity $v$ at an angle $\alpha$ to the axis. The magnetic induction of the field is equal to $BA$ screen is oriented at right angles to the axis and is located at a distance $1$ from the point $a$. Find the distance from the axis to the point on the screen into which the electron strikes.
When current breaks in primary coil current reaches to zero in second. Emf induced in the secondary coil is 20,000V and mutual inductance between the coils is 5H. The maximum current is the primary before the break is
Two conducting circular loops of radii $R _{1}$ and $R _{2}$ are placed in the same plane with their centres coinciding. If $R _{1} \gg R _{2}$, the mutual inductance $M$ between them will be directly proportional to
The mutual inductance $M _{12}$ of coil 1 with respect to coil 2
A long solenoid of diameter $0.1\ m$ has $2 \times {10^4}$ turns per metre.At the centre of the solenoid, a coil of $100$ turns and radius $0.01\ m$ is placed with its axis coinciding with the solenoid axis.The current in the solenoid reduces at a constant rate to $0\ A$ from $4\ A$ in $0.05\ s$. If the resistance of the coil is $10 \ {\pi ^2}\Omega ,$ the total charge flowing through the coil during this time is.
Two coils, a primary of $400$ turns and a secondary of $20$ turns are wound over an iron core of length $20\pi\ cm$ and cross-section of $2\ cm$ radius. If $\mu _{r}=800$, then the coefficient of mutual induction is approximately
A charge of ${10^{ - 6}}C$ is describing a circular path of radius $1$ cm making $5$ revolution per second . The magnetic induction field at the centre of the circle is
Two coils A and B have mutual inductance $2\times { 10 }^{ -2 }$ henry. If the current in the primary is $i=5\sin { \left( 10\pi t \right) } $ then the maximum value of e.m.f.induced in coil B is
When the primary current in the spark-coil of a car changes from $4A$ to zero in $10\mu s$, an emf of $40000$V is induced in the secondary. The mutual inductance between the primary and the secondary winding of the spark-coil will be-
Two coils A and B have mutual inductance $2\times { 10 }^{ -2 }$ henry. If the current in the primary is $i=5\sin { \left( 10\pi t \right) } $ then the maximum value of e.m.f. induced in coil B is
The electric field of an electromagnetic wave is given by, $E=(50N^{-1})\, \sin { \omega } (t-x/c)$. Find the energy contained in a cylinder of cross section $10cm^2$ and length $50 cm$ along the x-axis.
An electron having kinetic energy T is moving in a circular orbit of radius R perpendicular to a uniform magnetic induction $\vec { \mathrm { B } }$ If kinetic energy is doubled and magnetic induction tripled, the radius will
An average induced emf of 0.4 V appears in a coil when the current in it is changed from 10 A in one direction to 10 A in opposite direction in 0.5 sec. self-inductance of the coil is.
At any instant t currenetI thorugh a coil of sself inductance 2mH is given.The induced e.m.f will be zero at time
When a current of 5 A flows in the primary coil then the flux linked with the secondary coil is 200 weber. The value of coefficient of mutual induction will be
A cylindrical magnet is kept along the axis of a circular coil. On rotating the magnet about its axis. the coil will have induced in it
A coil of insulating wire is connected to battery. If it is moved towards a galvanometer then its point gets deflected because
Two coils P and Q are lying parallels and very close to each other. Coil P is connected to an AC source whereas Q is connected to a sensitive galvanometer. On pressing key K
The value of mutual inductance can be increased by
A long straight wire is placed along the axis of a circular ring of radius R. Then mutual inductance of this system is
A coil of wire has 0.2 m radius and 500 turns. It carries a current of 1 A.The magnetic induction at the centre of the coil is
The current in a coil is changed from 5 A to 10 A in $10^{-2}s$. Then, an emf of 50 m V is induced in a coil near by it. Calculate mutual inductance of two coils.
A short solenoid of radius $a,$ number of turns per unit length $n _ { 1 } ,$ and length $L$ is kept coaxially inside a very long solenoid of radius $b ,$ number of turns per unit length $n _ { 2 } .$ What is the mutual inductance of the system?
A long straight wire is placed along the axis of a circular ring of radius $R$. The mutual inductance of this system is
Two coils $A$ and $B$ having turns $300$ and $600$ respectively are placed near each other, on passing a current of $3.0$ ampere in $A$ the flux linked with $A$ is $1.2 \times 10 ^ { - 4 } weber$ and with $B$ it is $9.0 \times 10 ^ { - 5 } weber.$ The mutual inductance of the system is
The inductance of a solenoid $0.5\ m$ long of cross-sectional area $20\ cm^2$ and with $500$ turns is
Two coils are placed close to each other. The mutual inductance of the pair of coils depend upon :
Which of the following units denotes the dimension $\dfrac {ML^2}{Q^2}$ where Q denotes the electric charge?
The mutual inductance between two coils when a current of $5$ A changes to $10$ A in $1$ s and induces an emf of $100$ m V in the secondary is ______
Identify which of the following best describe the Mutual inductance?
For a current carrying inductor, emf associated in $20mV$. Now, current through it changes from $6A$ to $2A$ in $2s$. The coefficient of mutual inductance is
Two coils have a mutual inductance of $0.005\ H$. The current changes in the first coil according to equation $I=I _0sin\omega t$, where $I _0=10A$ and $\omega=100\pi rad/s$. The maximum value of emf (in volt) in the second coil is.
The mutual inductance of the system of two coils is $5mH$. The current in the first coil varies according to the equation $I={ I } { o }\sin { wt } $ where ${ I } _{ o }=10A$ and $W=100\pi \, rad/s$. The value of maximum induced emf in the second coil is ______
A short solenoid of length $4cm$, radius $2cm$ and $100$ turns is placed inside and on the axis of a long solenoid of length $80cm$ and $1500$ turns. A current of $3A$ flows through the short solenoid. The mutual inductance of two solenoids is
When the current in a coil changes from 8 ampere to 2 ampere in $3 \times 10^{-2}$ second, the e.m.f. induced in the coil is 2 volt. The self inductance of the coil (in millinery) is
Two coils have mutual inductance $0.005 H$. The current changes in the form coil according to equation, $ I = I _0 \sin \omega t . $ Where $ I _0 = 10 A. $ and $ \omega = 100 \pi $ rads/s. The maximum value of emf in the second coil is :
A coil of area 500 $cm^2$ having 1000 turns is placed such that the plane of the coil is perpendicular to a magnetic field of magnitude $4 \times 10^{-5}$ $weber/m^2$. If it is rotated by 180 about an axis passing through one of its diameter in 0.1 sec, find the average induced emf.
A long straight wire is placed along the axis of a circular ring of radius $R$. The mutual inductance of this system is
A coil of $Cu$ wire (radius $-r$, self-inductance-$L$) is bent in two concentric turns each having radius $\dfrac{r}{2}$. The self-inductance is now
Mutual inductance of a system of two thin coaxial conducting loops of radius 0.1 m, and then center separated by distance 10 m is (Take $\mu^{2} = 10$)
A ring of radius $r$ is uniformly charged with charge $q.$ If the ring is rotated about it's axis with angular frequency $\omega$, then the magnetic induction at its centre will be-
Give the MKS units for the following quantities.
Magnetic Induction.
Two coaxial coils are very close to each other and their mutual inductance is $5mH$. If a current $50\sin{500t}$ is passed on one of the coils then the peak value of induced emf in the secondary coil will be:
A solenoid would over a rectangular frame. If all the linear dimensions of the frame are increased by a factor $3$ and the number of turns per unit length remains the same, the inductance increased by a factor of :-
Two different coils have self inductance $L _{1}=8\ mH, L _{2}=2\ mH$. The current in the second coil is also increased at the same constant rate. The current in the second coil is also increased at the same constant rate. At a certain instant of time, the power given to the two coil is the same. At that time, the current, the induced voltage and the energy stored in the first coil are $i _{1}, V _{1}$ and $W _{1}$ respectively. Corresponding values for the second coil at the same instant are $i _{2}, V _{2}$ and $W _{2}$ respectively. Then
Two coils A and B having turns 300 and 600 respectively are placed near each other, on passing a current of 3.0 ampere in A, the flux linked with A is 1.2 x $10^{-4}$ weber and with B it is 9.0 x $10^{-5}$ weber. The mutual induction of the system is:
Two coaxial solenoids are made by winding thin insulated wire over a pipe of cross-sectional area $A=10cm^2$ and length $=20cm$. If one of the solenoids has $300$ turns and the other $400$ turns, their mutual inductance is $\left(\mu _o=4\pi\times 10^{-7} TmA^{-1}\right)$
A $50\ Hz$ ac current of peak value $2$ A flows through one of the pair of coils. If the mutual inductance between the pair of coils is $150\ mH$. then the peak value of voltage induced in the second coil is
The self-inductances of two identical coils are $0.1\ H$. They are wound over each other. Mutual inductance will be-
The length of solenoid is 0.3 m and the number of turns is 2000. The area of cross-section of the solenoid is $1.2\times 10^{-3} m^2$. Another coil of turns 200 is wrapped over the solenoid. a current of 2 A is passed through the solenoid and its direction is changed in 0.25 sec. Then the induced emf in the coil:
A coil of radius $1\ cm$ and of turns $100$ is placed in the middle of a long solenoid of radius $5\ cm$ and having $5\ turns/ cm$. The mutual induction in millihenry is
When 100 volts d.c. is applied across solenoid a current of 1.0 amp flows in it. When 100 volts a.c. is applied across the same coil, the current drops to 0.5 amp. If the frequency of the a.c. source is 50 Hz the impedance and inductance of the solenoid are
The inductance of a solenoid 0.5 m long of cross-sectional area $420 cm^{2}$ and with $500$ turns is
A current I flows in an infinity long wire with cross section in the from of a semicircular ring of radius R the magnitude of the magnetic induction along its axis is :-
What is inductance of a 25 cm long solenoid if it has 1000 turns an radius of its circular cross-section is 5 cm ?
A coil of mean area 500 $cm^2$ and having 1000 turns is held perpendicular to a uniform field of 0.4 gauss. The coil is turned through $180^o$ in $\frac{1}{10}$second. The average induced e.m.f. :-
The M.I. of a disc about its diameter is $2$ units. Its M.I. about axis through a point on its rim in the plane of the disc is
A ring of radius r is uniformly charged with charge $q$ . If the ring is rotated about it's axis with angular frequency $\omega$, then the magnetic induction at its centre will be-
The self inductance of a coil having $500$ turns is $50$ mH. The magnetic flux through the cross-sectional area of the coil while current through it is $8$mA is found to be?
What is the mutual inductance of coil and solenoid if a solenoid of length $0.50\ m$ and with $5000$ turns of wire has a radius $4\ cm$ and a coil of $700$ turns is wound on the middle part of the solenoid?
The mutual inductance of an induction coil is 5 H. In the primary coil, the current reduces from 5 A to zero in $10^{-3} s$. What is the induced e.m.f. in the secondary coil?
Two concentric rings are kept in the same plane. Number of turns in each rings is $25$. Their radii are $50 cm$ and $200 cm$ and they carry electric currents of $0.1 A$ and $0.2 A$ respectively, in mutually opposite directions. The magnitude of the magnetic field produced at their centre is ____________ $T$.
A solenoid of length 30 cm with 10 turns per centimetre and area of cross-Section 40 $cm^2 $completely surrounds another co-axial solenoid of same length, area of Cross-section 20 $cm^2$ with 40 turns per centimetre. The mutual inductance of the
A 2 m long solenoid with diameter 2 cm an 2000 turns has a secondary coil of 1000 turns wound closely near its midpoint. The mutual inductance between the two coils is
A pair of adjacent coils has a mutual inductance of 2.5 H. If the current in one coil changes from 0 to 40 A in 0.8 s, then the change in flux linked with the other coil is then
A short solenoid of radius a, number of turns per Unit length $n _1$. and length L is kept coaxially inside a very long solenoid of radius b, the number of turns per Unit length $n _2$. What is the mutual inductance of the system?
Two short bar magnets of magnetic moment 'M' each are arranged at the opposite corners of a square of side 'o', such that their centres coincide with the square. If the like poles are in the same direction, the magnetic induction at any of the other of the square is
A conducting ring of radius r and resistance R rolls on a horizontal surface with constant velocity v.
Two coils of self-inductances $2\ mH$ and $8\ mH$ are placed so close together that the effective flux in one coil is completely linked with the other. The mutual inductance between these coils is:
Mutual inductance of a system of two thin coaxial conducting loops of radius each, their centers separated by distance $d (d >>r)$ is
The coefficient of mutual inductance, when magnetic flux changes by $\displaystyle 2\times { 10 }^{ -2 }Wb$ and current changes by 0.01 A is :