Question

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

Answer 1

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