5.1 Describe the term impedance with reference to an RLC circuit - NSC Electrical Technology Power Systems - Question 5 - 2017 - Paper 1

In the given phasor diagram, the voltage across the inductor ($V_L = 80 V$) is greater than that across the capacitor ($V_C = 50 V$). This indicates that the circuit is inductive because the current ($I_T$) lags behind the voltage ($V_S$). Therefore, the overall circuit displays behavior characteristic of a resistive-inductive nature.

Increasing the supply frequency will result in a rise in the inductive reactance ($X_L$) of the circuit, which is directly proportional to frequency. Consequently, as $X_L$ increases, the voltage across the inductor $V_L$ will also increase, due to the relationship defined by $V_L = I_L imes X_L$.

The total voltage $V_T$ in a series RLC circuit can be calculated using the formula: V_T = ext{sqrt}igg{(}V_R^2 + (V_L - V_C)^2igg{)} Substituting the given voltages: V_T = ext{sqrt}igg{(}110^2 + (80 - 50)^2igg{)} = ext{sqrt}igg{(}110^2 + 30^2igg{)} = ext{sqrt}(12100 + 900) = ext{sqrt}(13000) = 114.02 V

The total current $I_T$ in a parallel circuit is calculated using the formula: $I_T = ext{sqrt}(I_R^2 + (I_L - I_C)^2)$ Given the currents:

• $I_R = 5 A$
• $I_L = 6 A$
• $I_C = 4 A$ We have: $I_T = ext{sqrt}(5^2 + (6 - 4)^2) = ext{sqrt}(5^2 + 2^2) = ext{sqrt}(25 + 4) = ext{sqrt}(29) = 5.39 A$

The phase angle $heta$ can be calculated using: heta = ext{cos}^{-1}igg{(}rac{I_R}{I_T}igg{)} Substituting the values:

The inductive reactance $X_L$ can be derived using the formula: X_L = rac{V_T}{I_L} By substituting the values: X_L = rac{240}{6} = 40 ext{ ohms}