A 25mF capacitor, 0 10H inductor and 25Ω resistor are connected in series with a c source whose emf - Physics - Electromagnetic Induction

Question

A 25mF capacitor, 0 10H inductor and 25Ω resistor are
connected in series with a c source whose emf is e=310sin314t(volt)
Find the following 1 Frequency of the source 2 Reactance of the
circuit 3 Impedance 4 Current in the circuit 5 Phase angel of the
current by which it leads or lags the applied emf 6 Expression for
the instantaneous current 7 Construct a phasor diagram for these
voltages 8 What value of inductance will make the impedance of the
circuit minimum?[

Krishan Yadav · Accepted Answer

Dear Student,given  e=310sin314t(volt)C =25mF L =0
10HR = 25 ohm1)comparing e with  x = Asinωt frequency  = ω2π =3142π =50 Hz2)Reactance  =XL - XC =ωL - 1ωC =314 × 0
1 -1314×25×10-3 =31 4 - 0
127 =31
27 ohm3)Impedance=Z = R2 +(XL - XC)2 =625 +977
81 = 1602 81 =40
035 ohm4) Irms = Io2Io = VoZ =31040
035= 7 74 A Irms =7 74 2 = 5
5 A5)φ =  tan-1(XL - XCR) =tan-1(40
03525) 6)instantaneous  current in the circuit I = Io sin(ωt +φ) I = 7
74sin(ωt +tan-1(40
03525))8)for minimum impedance circuit must be in resonance i
e
314 =1LCL=1314 × 314 ×25 × 10-3 =0
41mH

7)

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