In a Norton to Thevenin transformation, what are the relationships between I_N, V_th, and R_th?

In a Norton to Thevenin transformation, what are the relationships between I_N, V_th, and R_th?

• A. I_N equals V_th, and R_N equals R_th
• B. I_N equals V_th * R_th, and R_N equals R_th
• C. I_N = V_th / R_th; R_N = R_th
• D. I_N = V_th / (R_th + 1), R_N = R_th

Answer: (C)

When you convert between Norton and Thevenin, the goal is to keep the same behavior at the external terminals: the same voltage for a given load and the same current for a given shorted connection, which means the same resistance seen by the load. In Norton form you have a current source in parallel with a resistor, and in Thevenin form you have a voltage source in series with a resistor. The two representations are equivalent if their resistances match, and the current and voltage relate through Ohm’s law. The short-circuit current that would flow into a direct connection (the Norton current) equals the open-circuit voltage divided by the resistance: IN = Vth / Rth. Since the resistance is the same in both forms, RN = Rth. So the correct relationships are IN = Vth / Rth and RN = Rth.

When you convert between Norton and Thevenin, the goal is to keep the same behavior at the external terminals: the same voltage for a given load and the same current for a given shorted connection, which means the same resistance seen by the load.

In Norton form you have a current source in parallel with a resistor, and in Thevenin form you have a voltage source in series with a resistor. The two representations are equivalent if their resistances match, and the current and voltage relate through Ohm’s law.

The short-circuit current that would flow into a direct connection (the Norton current) equals the open-circuit voltage divided by the resistance: IN = Vth / Rth. Since the resistance is the same in both forms, RN = Rth.

So the correct relationships are IN = Vth / Rth and RN = Rth.