coil of reactance 100 ohm and resistance 100 ohm is connected to a 240 V, 50 Hz a.c. supply.(a) What is the maximum current in the coil ?(b) What is the time lag between the voltage maximum and t
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12th
Physics
Alternating Current
Basics of AC
A coil of inductance 0.50 H...
PHYSICS
A coil of inductance 0.50 H and resistance 100Ω is connected to a 240 V, 50 Hz ac supply.
(a) What is the maximum current in the coil?
(b) What is the time lag between the voltage maximum and the current maximum?
Hence, explain the statement that at very high frequency, an inductor in a circuit nearly amounts to an open circuit. How does an inductor behave in a dc circuit after the steady state?
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ANSWER
Given:
The inductance of the coil is 0.50H.
The resistance of the coil is 100Ω
The voltage supplied to the coil is 240V.
a)
The peak voltage supplied to the coil is given by:
V
o
=
2
V
The maximum current through the coil is given by:
I
o
=
R
2
+ω
2
L
2
V
o
I
o
=
10
4
+(100π×0.5)
2
2
×240
I
o
=1.3×10
−2
A
b)
The relation between the time lag and the inductance nad resistance of the coil is:
tanϕ=
R
ωL
tanϕ=
100
2π×50×0.5
tanϕ=1.571
⇒ϕ=57.5
o
ωt=57.5π/180
⇒t=3.19×10
−3
s