Question

In the circuit shown in the figure below, the ideal generator produces an rms voltage of 115 V when operated at 60 Hz. What is the rms voltage between the following points? Take R = 40 ohms, L = 145 mH, and C = 33

Answer 1

Impedence of the circuit is Z^2 = R^2 ?+(XL-Xc)^2

XL = wL = 2*3.14 * 60 * 0.145 = 54.63 ohms

Xc = 1/wC = 1/(2*3.14 * 60* 33e-6) = 80.42 ohms

so

Z^2 = 40^2 + (80.42-54.63)^2

Impedence Z^2 = 2265.1241

Z = 47.59 ohms

current i   = V/Z = 115/47.59 = 2.416 Amps

so

across AB, V = iXL = 2.416 * 54.63 = 132 V

across BC, V = iR   = 2.416 *40 = 96.64 volts

across CD, V = iXC = 2.416 * 80.42 = 192.29 Volts

across AC,

net Impedence Z^2 = R^2 = XL^2

Z^2   = 40^2 + 54.63^2

Z = 67.7 ohms

so V across AC = iZ = 2.416 * 67.7 = 163.58 Volts

across BD, Z^2 = R^2 + XC^2

Z^2 = 40^2   + 80.42^2

Z = 89.8 ohms

so across BD = iZ = 2.416 * 89.8

V = 217 Volts