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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.
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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
Define self-inductance. Write its SI units.
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Define self-inductance of a coil. Show that magnetic energy required to build up the current I in a coil of self inductance L is given by `1/2 LI^2`
Consider the self-inductance per unit length of a solenoid at its centre and that near its ends. Which of the two is greater?
An inductor-coil carries a steady-state current of 2.0 A when connected across an ideal battery of emf 4.0 V. If its inductance is 1.0 H, find the time constant of the circuit.
Two coils of self inductances 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 ______.
The self-inductance associated with a coil is independent of ______.
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 |
The current in a coil changes from 50A to 10A in 0.1 second. The self inductance of the coil is 20H. The induced e.m.f. in the coil is ______.
