Final answer:
The sending end voltage (Vs) and current (Is) equations with respect to impedance and receiving end variables can be written using components of impedance such as resistance (R) and reactance (X). The formulas are Vs = VR + Is * Zs and Is = IR, where Zs includes all series resistances and reactances in the circuit.
Step-by-step explanation:
To write the sending end voltage (Vs) and current (Is) equations with respect to impedance (R, X, Y) and receiving end current and voltage (VR, IR), we need to account for the impedance of the circuit. Impedance (Z) is composed of resistance (R) and reactance (X), which for an AC circuit may include inductive reactance (X₁) and capacitive reactance (Xc). The formula for impedance in terms of resistance and reactance is Z = R + jX, where 'j' is the imaginary unit.
The relationship between the sending and receiving end variables can be expressed as follows:
Vs = VR + Is * Zs
Is = IR
Here, Zs is the series impedance at the sending end of the circuit, including all resistances and reactances. VR is the voltage at the receiving end, and IR is the current at the receiving end. The voltage across each component (R₁, R₂, R3) in the circuit would be V₁ = IR₁, V₂ = IR₂, and V3 = IR3 respectively, where I is the total current flowing through the circuit as given by Ohm's Law.