Advertisements
Advertisements
Question
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.
Advertisements
Solution
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
RELATED QUESTIONS
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
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)
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 ______.
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 ______.
A coil of wire of a certain radius has 600 turns and a self-inductance is 108 mH. The self-inductance of a second similar coil of 500 turns will be:
The inductance of a solenoid L having diameter d. Let n be the number of turns per unit length. The inductance per unit length near the middle of a solenoid is ______.
(Assume that, l = current passes through the turns, µ0 = Permeability of vacuum)
A toroid of a circular cross-section of radius 0.05 m has 2000 windings and a self-inductance of 0.04 H. What is (a) the current through the windings when the energy in its magnetic field is 2 × 10−6 J and (b) the central radius of the toroid?
Two inductor coils with inductance 5 mH and 15 mH are connected in parallel. The resultant inductance of the combination of the two coils is ______.
