In a Thevenin equivalent with a load R_L in series, which expressions correctly give the current and the load voltage?

• A. I = V_th * R_L / (R_th + R_L); V_L = I * R_th
• B. I = V_th / (R_th + R_L); V_L = I * R_L
• C. I = V_th / R_th; V_L = V_th - I*R_th
• D. I = V_th / (R_th - R_L); V_L = I * R_L

Answer: (B)

In a Thevenin circuit with the load in series, the current is determined by the total resistance in the loop. The current flowing through both the Thevenin resistance and the load must satisfy Ohm’s law for the entire path: I = V_th / (R_th + R_L). The voltage across the load is the current times the load resistance, so V_L = I × R_L. Substituting the expression for I gives V_L = V_th × R_L / (R_th + R_L).

This choice is the best because it uses the correct total resistance in the current expression and places the voltage across the load, as the current through a series circuit flows through both elements and the load voltage is the portion of the source voltage that drops across R_L.

The other forms mix up where the voltage and current appear, omit the load, or use an incorrect sign in the denominator, leading to inconsistent or unreal results.