A (solenoid) coil is wound on a core of square cross-section. If all the linear dimensions of core are increased 2 times, but the number of turns per unit length of the coil, remains same, the self-inductance would increases by a factor of

Magnetic flux, through a stationary loop, with a resistance R, varies during the time internal ${}^{\mathrm{\prime }}{\tau }^{\mathrm{\prime }}\text{'}\backslash tau\text{'}$ as $\varphi =at(\tau -t)\backslash phi=at(\backslash tau-t)$ where a is a constant. The amount of of heat generated in the loop, during time internal, $\tau \backslash tau$ , would be

A conducting circular loop is placed in a uniform magnetic filed (of induction ‘B’tesla), with its plane normal to the field. If the radius of the loop were to start shrinking at a constant rate $\frac{dr}{dt}\backslash frac\{dr\}\{dt\}$. The induced emf, at the instant when its radius is ‘r’, would be

A conducting rod of length L lies along the y–axis with one end at origin and the other end at (0, L, 0). There is a magnetic field $B=B_{0}y\widehat{k}B=B\_0y\backslash hat\; k$ in that region. If the rod moves with a velocity $V=V_0\widehat{i},V=V\_0\backslash hat\; i,$ the e.m.f induced between the ends of the rod will be

The coefficient of mutual inductance of two circuits A and B is 3 mH and their respective resistances are 10$\mathrm{\Omega }\backslash Omega$ and 4 ohm. How much should the currents change, in 0.02 second, in circuit A, so that an induced current 0.006 ampere flows through the circuit B?

A series LCR circuit can bring about a ‘voltage magnification’, of the voltage of the a.c. source connected across it, provided the frequency, of the a.c. voltage source equals

A step-down transformer (having windings of negligible resistance) is used to step down the mains voltage of 220V, to22V to operate a device of impedance $220\mathrm{\Omega }220\backslash ,\backslash Omega$. Assuming an efficiency of 80%, the current flowing in the primary coil of two transformer is

For a pure inductor, or a pure capacitor, connected to an a.c. voltage source, one can say that the instantaneous power.

The inductance, capacitance and resistance in a given series LCR circuit, have values of (n) henry, $\left(\frac{1}{n^3}\right)\backslash left(\backslash frac\; \{1\}\{n^3\}\backslash right)$ farad, and $(n^2)(n^2)$ohm. The quality factor, Q, and the resonant frequency $(V_0)(V\_0)$, of this circuit, equal, respectively,

It is required to improve the sharpness of resonance of a series LCR circuit by a factor of 4. This requirement can be met by