Advertisements
Advertisements
प्रश्न
Answer the following question.
When an inductor is connected to a 200 V dc voltage, a current at 1A flows through it. When the same inductor is connected to a 200 V, 50 Hz ac source, only 0.5 A current flows. Explain, why? Also, calculate the self-inductance of the inductor.
उत्तर
When the inductor is connected across the 200 V DC circuit 1 A current flows because in this case the inductor simply acts as a resistor and there is no inductive reactance. Whereas, when we connect the same inductor across 200 V AC, due to inductive reactance the overall impedance is changed and hence the value of current also changes.
When the inductor is connected across 200 V DC
The resistance of the coil
`R = 200/1 = 200 Ω`
Let the self-inductance of the inductor be L,
When the inductor is connected across 200 V A.C.
Net impedance, Z = `sqrt((2pifL)^2 + R^2) = 200/0.5 = 400 Omega`
⇒ `(2pi xx 50 xx L)^2 + 200^2 = 400^2`
⇒ `(100piL)^2 = 160000 - 40000`
⇒ `10000pi^2L^2 = 120000`
⇒ `L^2 = 12/pi^2`
`therefore L = sqrt(12)/pi H`
संबंधित प्रश्न
The currents flowing in the two coils of self-inductance L1 = 16 mH and L2 = 12 mH are increasing at the same rate. If the power supplied to the two coil is equal, find the ratio of induced voltages ?
The currents flowing in the two coils of self-inductance L1 = 16 mH and L2 = 12 mH are increasing at the same rate. If the power supplied to the two coil is equal, find the ratio of the currents ?
Define self inductance. Write its S.I. units.
Two solenoids have identical geometrical construction but one is made of thick wire and the other of thin wire. Which of the following quantities are different for the two solenoids?
(a) self-inductance
(b) rate of Joule heating if the same current goes through them
(c) magnetic field energy if the same current goes through them
(d) time constant if one solenoid is connected to one battery and the other is connected to another battery.
Obtain an expression for the self-inductance of a solenoid.
When the number of turns in a coil is tripled without any change in the length of the coil, its self-inductance ______
A toroidal solenoid with air core has an average radius 'R', number of turns 'N' and area of cross-section 'A'. The self-inductance of the solenoid is (Neglect the field variation cross-section of the toroid)
Energy needed to establish an alternating current I in a coil of self-inductance L is
Calculate the self-inductance of a coil using the following data obtained when an AC source of frequency `(200/pi)` Hz and a DC source are 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 |
Obtain an expression for the self inductance of a solenoid.
