Mutual Inductance

Two coils $P$ and $Q$ are separated by some distance. When a current of $3\text{ A}$ flows through coil $P$, a magnetic flux of $10^{-3}$ Wb passes through $Q$. No current is passed through $Q$. When no current passes through $P$ and a current of $2\text{ A}$ passes through $Q$, the flux through $P$ is $x \times 10^{-3}$ Wb. The value of $x$ is

A current $i = 10\sin(100\pi t)$ A is passed in first coil, which induces a maximum e.m.f. $5\pi$ V in second coil. The mutual inductance between the coils is

Consider two coils in which a current in one coil carrying $6$ A causes the change in the flux in the second coil $12 \times 10^{-4}$ weber/turn. The second coil has $2000$ turns. The mutual inductance between the coils is

Two coils have a mutual inductance of $0.005$ H. The current changes in the first coil according to equation $I = I_0 \sin \omega t$, where $I_0 = 10$ A and $\omega = 60\pi$ rad s${}^{-1}$. The maximum values of e.m.f. in the second coil in volt will be

The coefficient of mutual induction is $3$H and induced e.m.f. across secondary is $4$ kV. Current in primary is reduced from $7$A to $2$A. The time required for the change of current is

Two coils P and Q have mutual inductance 'M' H. If the current in the coil P is $I = I_0 \sin \omega t$, then the maximum value of e.m.f. induced in coil Q is

Alternating current of peak value $\left(\frac{2}{\pi}\right)$ A flows through the primary coil of a transformer. The coefficient of mutual inductance between primary and secondary coils is $1$ H. The peak em.f. induced in secondary coil is (Frequency of a. c. is $50$ Hz)

Two coils of self inductance, $2$ mH and $8$ mH are placed so closed together that the effective flux in one coil is completely linked with the other. The mutual inductance between these coils is,

Two coils having self-inductance $L_1 = 75$ mH and $L_2 = 48$ mH are coupled with each other. If the mutual inductance of the coils is 37.2 mH, then coefficient of coupling will be

Two conducting circular loops of radii $r_1$ and $r_2$ are placed in the same plane with their centres coinciding. If $r_1 \gg r_2$, then the mutual inductance $M$ between them is proportional to [$I_1 =$ current flowing through coil 1 and $I_2 =$ current flowing through coil 2]

Two conducting circular loops of radii $r$ and $2r$ are placed in the same plane with their centres coinciding. The mutual inductance $M$ between them is {same current is passing through both the coils} ($\mu_0 =$ permeability of free space)

Two planar concentric rings of metal wire having radii '$r_1$' and '$r_2$' (with $r_1 > r_2$) are placed in air. The current 'I' is flowing through the coil of larger radius. The mutual inductance between the coils is given by ( $\mu_0$ = permeability of free space)

A circular coil of radius 'r' is placed on another circular coil whose radius is 'R' and the current flowing through it is changing and their centers coincide. ($R \gg r$). If both the coils are coplanar, then the mutual inductance between them is proportional to

Two concentric circular coils having radii $r_1$ and $r_2$ ($r_2 \ll r_1$) are placed co-axially with centres coinciding. The mutual inductance of the arrangement is (Both coils have single turn, $\mu_0$ = permeability of free space)

A circular current loop of radius $R$ is placed inside square loop of side length $L$ ($L \gg R$) such that they are co-planar and their centers coincide. The permeability of free space is $\mu_0$. The mutual inductance between circular loop and square loop is ______.

Suppose a long solenoid of 100 cm length, radius 2 cm having 500 turns per unit length, carries a current $I = 10 \sin(\omega t)\text{ A}$, where $\omega = 1000\text{ rad/s}$. A circular conducting loop $(B)$ of radius 1 cm coaxially slided through the solenoid at a speed $v = 1\text{ cm/s}$. The r.m.s. current through the loop when the coil $B$ is inserted 10 cm inside the solenoid is $\frac{\alpha}{\sqrt{2}} \mu A$. The value of $\alpha$ is ______. [Resistance of the loop $= 10\,\Omega$ ]

Two coils P and Q are kept near each other. When no current flows through coil P and current increases in coil Q at the rate $10\text{ A/s}$, the emf in coil P is 12 mV. When coil Q carries no current and current of 1.5 A flows through coil P, the magnetic flux linked with the coil Q in mWb is

When magnetic flux changes from $6.5 \times 10^{-2}\text{ Wb}$ to $11 \times 10^{-2}\text{ Wb}$ and the change in current is 0.03 A, the coefficient of mutual inductance will be

Two coils $P$ and $Q$ are kept near each other. When no current flows through coil $P$ and current increases in coil Q at the rate of $10\text{ A/s}$, the e.m.f. in coil P is 15 mV. When coil Q carries no current and current of 1.8 A flows through coil $P$, the magnetic flux linked with coil Q is

The coefficient of mutual induction is 2 H and induced e.m.f. across secondary is 2 kV. Current in the primary is reduced from 6 A to 3 A. The time required for the change of current is

Two planar concentric rings of metal wire having radii $r_1$ and $r_2 \ (r_1 > r_2)$ are placed in air. The current I is flowing through the coil of larger radius. The mutual inductance between the coils is given by ( $\mu_0 =$ permeability of free space)

Two conducting circular loops of radii $R_1$ and $R_2$ are placed in the same plane with their centres coinciding. If $R_1 > R_2$, the mutual inductance M between them will be directly proportional to

Consider I1 and I2 are the currents flowing simultaneously in two nearby coils 1 & 2, respectively. If L1 = self inductance of coil 1, M12 = mutual inductance of coil 1 with respect to coil 2, then the value of induced emf in coil 1 will be:

The coefficient of mutual induction is 2 H and induced e.m.f. across secondary is 2 kV. Current in the primary is reduced from 6 A to 3 A. The time required for the change of current is

Two coils have a mutual inductance 0.003 H. The current changes in the first coil according to equation $I = I_0 \sin \omega t$, where $I_0 = 8\text{ A}$ and $\omega = 100\pi\text{ rad s}^{-1}$. The maximum value of e.m.f. in the second coil is

Two coils have a mutual inductance $5 \times 10^{-3}\text{ H}$. The current changes in the first coil according to the equation $I_1 = I_0 \sin \omega t$ where $I_0 = 10\text{ A}$ and $\omega = 100\pi\text{ rad/s}$. What is the value of the maximum e.m.f. in the coil?

Two coils are kept near each other. When no current passes through first coil and current in the $2$nd coil increases at the rate $10\text{ A/s}$, the e.m.f. in the $1$st coil is 20 mV. When no current passes through $2$nd coil and 3.6 A current passes through $1$st coil the flux linkage in coil 2 is

Two coils have mutual inductance $0.002\text{ H}$. The current changes in the first coil according to the relation $i = i_0 \sin \omega t$, where $i_0 = 5\text{ A}$ and $\omega = 50\pi$ rad/s. The maximum value of emf in the second coil is $\frac{\pi}{\alpha}\text{ V}$. The value of $\alpha$ is _______.

The mutual inductance of two coils is 45 mH. The self-inductance of the coils are $L_1 = 75\text{ mH}$ and $L_2 = 48\text{ mH}$. The coefficient of coupling between the two coils is

Two coils of self-inductance 25 mH and 9 mH are placed close together such that the effective flux in one coil is completely linked with the other The mutual inductance between these coils is

Two concentric circular coils having radii ' $r_1$ and ' $r_2$ ' $(r_2 \ll r_1)$ are placed co-axially with centres coinciding. The mutual inductance of the arrangement is ( $\mu_0 =$ permeability of free space) (Both coils have single turn)

The planar concentric rings of metal wire having radii $r_1$ and $r_2$ (with $r_1 > r_2$) are placed in air. The current $I$ is flowing through the coil of larger radius. The mutual inductance between the coils is given by ( $\mu_0 =$ permeability of free space)

Two conducting circular loops A and B are placed in the same plane with their centres coinciding as shown in figure. The mutual inductance between them is:

The number of turns in the primary of a transformer are 1000 and in secondary 3000. If 80 V a.c. is applied to the primary, the potential difference per turn of the secondary coil is

A small square loop of wire of side $l$ is placed inside a large square loop of wire of side $L \left(L = l^2\right)$. The loops are coplanar and their centers coincide. The value of the mutual inductance of the system is $\sqrt{x} \times 10^{-7}\text{ H}$, where $x =$ _________.

Two coils have a mutual inductance of $0.004\text{ H}$. The current changes in the first coil according to equation $I = I_0 \sin \omega t$, where $I_0 = 10\text{ A}$ and $\omega = 50\pi\text{ rad s}^{-1}$. The maximum value of e.m.f. in the second coil in volt is

Two coils $A$ and $B$ have mutual inductance 0.008 $\text{H}$. The current changes in the coil A, according to the equation $I = I_m \sin \omega t$, where $I_m = 5\text{ A}$ and $\omega = 200\pi\text{ rad s}^{-1}$. The maximum value of the e.m.f. induced in the coil $B$ in volt is

The mutual inductance (M) of the two coils is $3\text{ H}$. The self inductances of the coils are $4\text{ H}$ and $9\text{ H}$ respectively. The coefficient of coupling between the coils is

A coil of radius '$r$' is placed on another coil (whose radius is $R$ and current flowing through it is changing) so that their centres coincide $(R \gg r)$. If both the coils are coplanar then the mutual inductance between them is ( $\mu_0 =$ permeability of free space)

Two concentric circular coils having radii $r_1$ and $r_2 \ (r_2 \ll r_1)$ are placed co-axially with centres coinciding. The mutual induction of the arrangement is (Both coils have single turn, $\mu_0 =$ permeability of free space)

Two conducting circular loops of radii '$R_1$' and '$R_2$' are placed in the same plane with their centres coinciding. If $R_1 > R_2$, the mutual inductance $M$ between them will be directly proportional to

The alternating e.m.f. induced in the secondary coil of a transformer is mainly due to

A transformer has 20 turns in the primary and 100 turns in the secondary coil. An ac voltage of $V$in $= 600 \sin 314 t$ is applied to primary terminal of transformer. Then maximum value of secondary output voltage obtained in volt is

The mutual inductance of a pair of coils, each of '$N$' turns, is '$M$' henry. If a current of '$I$' ampere in one of the coils is brought to zero in '$t$' second, the e. m. f. induced per turn in the other coil in volt is

Find the mutual inductance in the arrangement, when a small circular loop of wire of radius '$R$' is placed inside a large square loop of wire of side $L \ (L \gg R)$. The loops are coplanar and their centres coincide:

Two concentric circular coils with radii $1\text{ cm}$ and $1000\text{ cm}$, and number of turns 10 and 200 respectively are placed coaxially with centers coinciding. The mutual inductance of this arrangement will be ___________ $\times 10^{-8}\text{ H}$. (Take, $\pi^2 = 10$)

A square loop of side $2.0\text{ cm}$ is placed inside a long solenoid that has 50 turns per centimetre and carries a sinusoidally varying current of amplitude $2.5\text{ A}$ and angular frequency $700\text{ rad s}^{-1}$. The central axes of the loop and solenoid coincide. The amplitude of the emf induced in the loop is $x \times 10^{-4}\text{ V}$. The value of $x$ is __________.

(Take, $\pi = \frac{22}{7}$)

A small square loop of wire of side $l$ is placed inside a large square loop of wire $L (L \gg l)$. Both loops are coplanar and their centres coincide at point $O$ as shown in figure. The mutual inductance of the system is:

A current $I = 10\sin(100\pi t)$ ampere, is passed in a coil which induces a maximum emf $5\pi$ volt in neighbouring coil. The mutual inductance of two coils is

A coil of radius '$r$' is placed on another coil (whose radius is '$R$' and current through it is changing) so that their centres coincide. ( $R > r$ ). If both coplanar, then the mutual inductance between them is proportional to

Two conducting circular loops of radii R1 and R2 are placed in the same plane with their centres coinciding. If R1 >> R2, the mutual inductance M between them will be directly proportional to:

A small square loop of side 'a' and one turn is placed inside a larger square loop of side b and one turn (b >> a). The two loops are coplanar with their centres coinciding. If a current I is passed in the square loop of side 'b', then the coefficient of mutual inductance between the two loops is:

Two concentric circular coils, C1 and C2 are

placed in the XY plane. C1 has 500 turns, and

a radius of 1 cm. C2 has 200 turns and radius

of 20 cm. C2 carries a time dependent current

I(t) = (5t2 – 2t + 3) A where t is in s. The emf

induced in C1 (in mV), at the instant t = 1 s is

$\frac{4}{x}$. The value of x is ___.

Two coils have a mutual inductance of 0.01 H. The current in the first coil changes according to equation, $I = 5\sin 200\pi t$. The maximum value of emf induced in the second coil is

Two coils 'P' and 'Q' are separated by some distance. When a current of 3 A flows through coil 'P', a magnetic flux of 10–3 Wb passes through 'Q'. No current is passed through 'Q'. When no current passes through 'P' and a current of 2 A passes through 'Q', the flux through 'P' is :-

There are two long co-axial solenoids of same length $l$. The inner and outer coils have radii r1 and r2 and number of turns per unit length n1 and n2, respectively. The ratio of mutual inductance to the self - inductance of the inner-coil is:

At the center of a fixed large circular coil of radius R, a much smaller circular coil of radius r is placed. The two coils are concentric and are in the same plane. The larger coil carries a current I. The smaller coil is set to rotate with a constant angular velocity $\omega$ about an axis along their common diameter. Calculate the emf induced in the smaller coil after a time t of its start of rotation.

A small circular loop of wire of radius a is located at the centre of a much larger circular wire loop of radius b. The two loops are in the same plane. The outer loop of radius b carries an alternating current I = Io cos ($\omega$t). The emf induced in the smaller inner loop is nearly:

Two coils, X and Y, are kept in close vicinity of each other. When a varying current, $I(t)$, flows through coil X, the induced emf $(V(t))$ in coil Y, varies in the manner shown here. The variation of $I(t)$, with time, can then be represented by the graph labelled as graph:

(A)

(B)

(C)

(D)

A circular loop of radius $0.3\text{ cm}$ lies parallel to a much bigger circular loop of radius $20\text{ cm}$. The center of the small loop is on the axis of the bigger loop. The distance between their centers is $15\text{ cm.}$ If a current of $2.0\text{ A}$ flows through the smaller loop, then the flux linked with bigger loop is

Two coaxial solenoids are made by winding thin insulated wire over a pipe of cross-sectional area $A = 10\text{ cm}^2$ and length $= 20\text{ cm}$. If one of the solenoid has $300$ turns and the other $400$ turns, their mutual inductance is

$\left(\mu_0 = 4\pi \times 10^{-7}\text{ T m A}^{-1}\right)$

Two coils of self inductance 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

Two coils are placed close to each other. The mutual inductance of the pair of coils depends upon

Two coils have a mutual inductance of $0.005\text{ H}$. The current changes in the first coil according to equation $I = I_0 \sin \omega t$, where $I_0 = 10\text{ A}$ and $\omega = 100\pi\text{ rad/s}$. The maximum value of emf in the second coil is