If the flux associated with a coil varies at the rate of \(2\text{ Wb/min}\), then the induced emf in the coil is
From Faraday's law, the induced electromotive force is \(e = \frac{dPhi}{dt}\). Converting minutes to seconds: \(e = \frac{2\text{ Wb}}{60\text{ s}} = \frac{1}{30}\text{ V}\).
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 magnetic field produced by the larger loop 1 at the center is \(B_1 = \frac{\mu_0 I_1}{2 R_1}\). The magnetic flux through the smaller loop 2 is \(\phi_2 = B_1 A_2 = \frac{\mu_0 I_1}{2 R_1} \pi R_2^2\). Therefore, \(M = \frac{\phi_2}{I_1} = \frac{\mu_0 \pi R_2^2}{2 R_1}\), which means \(M \propto \frac{R_2^2}{R_1}\).
A step down transformer connected to an ac mains supply of \(220\text{ V}\) is made to operate at \(11\text{ V}\), \(44\text{ W}\) lamp. Ignoring power losses in the transformer, what is the current in the primary circuit?
Assuming zero power losses, the input power in the primary circuit equals the output power in the secondary circuit: \(P_{\text{in}} = P_{\text{out}} = 44\text{ W}\). Since \(P_{\text{in}} = V_p I_p\), we get \(I_p = \frac{P_{\text{in}}}{V_p} = \frac{44}{220} = 0.2\text{ A}\).
A coil has a self-inductance of 0.02 H. The current through it, is allowed to change at the rate of 4 A in \(2 \times 10^{-2}\text{ s}\). The e.m.f induced in the coil will be
Formula: \(e = L \frac{dI}{dt}\). Substituting \(L = 0.02\text{ H}\), \(dI = 4\text{ A}\) and \(dt = 2 \times 10^{-2}\text{ s}\), we get \(e = 0.02 \times 200 = 4\text{ V}\).
In an ideal transformer, the turns ratio is \(\frac{N_p}{N_s} = \frac{1}{3}\). The ratio of \(I_s : I_p\) is equal to (symbols carry their usual meaning):
For an ideal transformer, input power equals output power: \(V_p I_p = V_s I_s ⇒ \frac{I_s}{I_p} = \frac{V_p}{V_s} = \frac{N_p}{N_s} = \frac{1}{3}\).
The ratio of secondary to primary turns in a transformer is 4 : 1. If the power input is P, then output power neglecting all losses must be equal to
In an ideal transformer, there is no energy loss. Therefore, the output power is equal to the input power, which is P.
Assertion (A): A changing magnetic flux induces an electric field.
Reason (R): An inductor always tends to keep the flux constant.
Faraday's Law states a changing magnetic flux induces an electric field. Inductors oppose change in flux, but don't keep it constant. Hence, Assertion is true and Reason is false.
Assertion (A): When a circuit having large inductance is switched off sparking occurs at the switch.
Reason (R): Emf induced in an inductor is given by \( |\text{E}| = \text{L} |\frac{\text{di}}{\text{dt}}| \).
When a circuit with large inductance is switched off, \( \text{di/dt} \) is very large. This induces a large \( \text{EMF} = \text{L di/dt} \) across the inductor, causing sparking.
Assertion (A): A metal ring is kept on a cardboard on top of a fixed current carrying solenoid. If current in the solenoid is switched off, the upward reaction of card board on the ring will increase.
Reason (R): Induced current in the ring will be in the same direction as in the solenoid.
When solenoid current is switched off, flux decreases. Induced current in the ring flows in the same direction as solenoid current (Lenz's Law), causing attraction. This increases the upward reaction.
Assertion (A): If a cylindrical bar magnet is dropped through a metallic pipe, it takes more time to come down a similar unmagnetised cylindrical iron bar dropped through the same metallic pipe.
Reason (R): For the magnet, eddy currents are produced in the metallic pipe.
As the magnet falls, changing flux induces eddy currents in the pipe. These currents oppose the magnet's motion (Lenz's Law), creating a retarding force that slows it down.