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NCERT Class XII Chapter
Alternating Current
Questions With Solutions

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Question : 13 of 26
Marks: +1, -0
A coil of inductance 0.50 H and resistance 100 Ω 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?
Solution:  
Inductive reactance
XLX_L = 2πf L = 2π × 50 × 0.5 = 157 Ω
Impedence Ζ = R2+XL2\sqrt{R^2+X_L^2} = (100)2+(157)2\sqrt{(100)^2+(157)^2}
= 186.14 Ω
(a) Virtual current in the coil
IvI_v = EvZ\frac{E_v}{Z} = 240186.14\frac{240}{186.14} = 1.29 A
Maximum current, I0I_0 = Iv2I_v\sqrt{2} = 1.82 A
(b) Phase lag, tan ϕ = XLR\frac{X_L}{R} = 1.57
φ = tan⁡−1\tan^{-1} (1.57) = 57.5° or φ = 0.32 π radian
Time lag, t = φ/ω = 3.2 ms
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