Advertisements
Advertisements
प्रश्न
A current of 1A flows through a coil when it is connected across a DC battery of 100V. If the DC battery is replaced by an AC source of 100 V and angular frequency of 100 rad s-1, the current reduces to 0.5 A. Find
- the impedance of the circuit.
- self-inductance of coil.
- Phase difference between the voltage and the current.
उत्तर
Given: IDC = 1A, V = 100V, ω = 100 rad/sec.
IDC = `V/R ⇒ 100/R = 1`
R = 100 Ω
The a.c. flowing,
IAC = 0.5 A
- Impedance: Z = `sqrt(R^2 + (omegaL)^2`
when AC is applied.
Z = `V/I = 100/0.5 = 200 Omega` - Self-inductance of the coil:
We know `Z^2 = R^2 + X_L^2`
`X_L^2 = Z^2 - R^2`
= `(200)^2 - (100)^2`
= 40000 - 10000
XL = 173.21 Ω
XL = ωL
⇒ L = `X_L/omega = 173.21/100`
L = 1.73 H - The phase difference between V and I, (cosΦ):
`cosphi = R/L = 100/1.73`
`cosphi = 57.73`
`phi = cos^-1(57.73)`
APPEARS IN
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 the currents ?
Consider the self-inductance per unit length of a solenoid at its centre and that near its ends. Which of the two is greater?
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.
When a coil is connected to a D.C. source of e.m.f. 12 volt, then a current of 4 ampere flows in it. If the same coil is connected to a 12 volt, 25 cycle/s A.C sources, then the current flowing in it is 2.4 A. The self-inductance of the coil will be ______
Two rods of same material and volume having circular cross-section are subjected to tension T. Within the elastic limit, same force is applied to both the rods. Diameter of the first rod is half of the second rod, then the extensions of first rod to second rod will be in the ratio
Two coils of wire A and B are placed mutually perpendicular as shown. When current is changed in any one coil.
A resistance of 100 `Omega`, inductor of self-inductance`(4/pi^2)` H and a capacitor of unknown capacitance are connected in series to an a.c. source of 200 V and 50 Hz. When the current and voltage are in phase, the capacitance and power dissipated is respectively ____________.
When the current in a coil changes from 2 amp. to 4 amp. in 0.05 sec., an e.m.f. of 8 volt is induced in the coil. The coefficient of self inductance of the coil is ______.
A coil is wound on a frame of rectangular cross-section. If all the linear dimensions of the frame are increased by a factor 2 and the number of turns per unit length of the coil remains the same, self-inductance of the coil increases by a factor of ______.
If both the number of turns and core length of an inductor is doubled keeping other factors constant, then its self-inductance will be ______.
