(a) (i) Define coefficient of self-induction. Obtain an expression for self-inductance of a long solenoid of length $$l$$, area of cross- section A having $$\mathbf{N}$$ turns.
(ii) Calculate the self-inductance of a coil using the following data of obtained when an AC source of frequency $$\left(\frac{200}{\pi}\right) \mathrm{~Hz}$$ and a DC source is applied across the coil.
| AC Source | ||
|---|---|---|
| S.No. | V (Volts) | I(A) |
| 1 | 3.0 | 0.5 |
| 2 | 6.0 | 1.0 |
| 3 | 9.0 | 1.5 |
| DC Source | ||
|---|---|---|
| S.No. | V (Volts) | I(A) |
| 1 | 4.0 | 1.0 |
| 2 | 6.0 | 1.5 |
| 3 | 8.0 | 2.0 |
OR
(b) (i) With the help of a labelled diagram, describe the principle and working of an ac generator. Hence, obtain an expression for the instantaneous value of the emf generated.
(ii) The coil of an ac generator consists of 100 turns of wire, each of area $$0.5 \mathrm{~m}^2$$. The resistance of the wire is $$100 \Omega$$. The coil is rotating in a magnetic field of $$0.8 \mathrm{~T}$$ perpendicular to its axis of rotation, at a constant angular speed of 60 radian per second. Calculate the maximum emf generated and power dissipated in the coil.
(ii) Calculation of self inductance:
| DC SOURCE | ||||
|---|---|---|---|---|
| S. No. | V(Volts) | I(Ampere) | Resistance (Ohms) | Average resistance value (R) |
| 1 | 4.0 | 1.0 | 4.0 | $$4.0\Omega$$ |
| 2. | 6.0 | 1.5 | 4.0 | |
| 3 | 8.0 | 2.0 | 4.0 | |
| AC SOURCE | ||||
|---|---|---|---|---|
| S. No. | V(Volts) | I(Ampere) | Impedance (Ohms) | Average Impedance value (Z) |
| 1 | 3.0 | 0.5 | 6.0 | $$6.0\Omega$$ |
| 2. | 6.0 | 1.0 | 6.0 | |
| 3 | 9.0 | 1.5 | 6.0 | |