Find the voltage across the various elements, i.e., resistance, capacitance and inductance which are in series and having values 100Omega, 1muF and 2.0H, respectively. Given emf is V=100sqrt2sin1000t volt
Answers
Voltage across the resistance (Vr), capacitance (Vc) and inductance (Vl) which are in series are:
Vr =70.7V
Vc=70.7V
Vl=141.4 V
◆ Since V = 100√2 sin1000t ,
Vo = 100√2 V
◆ ROOT MEAN SQUARE VOLTAGE
Vrms = Vo/√2 =100 V
◆ ROOT MEAN SQUARE CURRENT
Irms = Vrms / Z ,
Where Z is the IMPEDANCE of the circuit including all the elements.
◆ Impedance Z is the total restriction to the flow of current.
◆Impedance Z of Capacitor ,
Xc = 1/wC, ( w , omega being the frequency; C is the capacitance)
Here, Xc = 1 / (1000× 10^-6 ) = 10^3.
◆ Impedance Z of Inductor,
Xl = wL (L is the inductance), Here
Xl = 1000×2 =2000
◆ Root mean square current ,
Irms = Vrms/Z,
◆Where total impedance
Z = [ R^2 + (Xc+ Xl)^2 ]^(1/2)
◆Given values,
R = 100Omega,
C = 1muF
L = 2.0H,
w , omega = 1000
◆On substitution ,
Irms = Vrms/[ R^2 + (Xc+ Xl)^2 ]^(1/2)
= 100 / [ 1000^2 + (10^3 + 2000)^2 ] ^(1/2)
= 0.0707 A
◆Thus,
Vr = Irms × R = 0.0707 × 1000
= 70.7 V
◆Vc = Irms × Xc = 0.0707 × 10^3
= 70.7V
◆Vl = Irms × Xl = 0.0707 × 2000
= 141.4 V