Question

1. A R-L circuit consists of one resistance 2.0 Ohm and one unknown Inductance. A voltage v=54 sin(399 t) is applied to this circuit and measured current is 2.77 A. Find out the unknown Inductance in mH unit.

2. In a R-L-C AC circuit, R= 7 Ohm, ZL= j 8 Ohm, ZC= -j 15 Ohm. Supply voltage is v= 15 sin( 7 t). Calculate the ANGLE of Z.

Answer 1

1.
The impedance of the circuit,
Z = V / I
Where V is the voltage and I is the current
= 54 / 2.77
= 19.49 Ohm

Z = SQRT[R² + ²L²]
Where R is the resistance, is the angular velocity, and L is the inductance.
Squaring the above equation,
Z² = R² + ²L^2
2L² = Z² - R²
L² = (Z² - R²) / ²
L = 1/ * SQRT[Z² - R²]
Substituting values,
L = 1 / 399 * SQRT[19.49² - 2²]
= 48.6 * 10^-3 H
= 48.6 mH

2.
= tan^-1[(Z_L - Z_C) / R
Where Z_L and Z_C are the inductive and capacitive reactances, R is the resistance.
Substituting values,
= tan^-1[(8 - (-15)) / 7]
= 73 degrees