Which Norton equivalent (current source and resistor) is equivalent to a voltage source with an EMF of 12 V and an internal resistance of 4 Ω?

Answer: A. A 3 A current source with 4 Ω in parallel

The Norton current source equals the current that flows when the terminals are shorted: 12 V/4 Ω = 3 A. The resistor is the same 4 Ω as the Thevenin resistance and goes in parallel with the current source. As a check, with the terminals open all 3 A flows through the 4 Ω, giving 3 A × 4 Ω = 12 V—the open-circuit voltage of the original source. Converting between voltage and current sources is a common way to simplify circuits.

• A. Correct. A current source equal to the short-circuit current, 12 V/4 Ω = 3 A, with 4 Ω in parallel.
• B. A resistor in series with a current source does not affect the terminal voltage–current relation, so this is not equivalent to the original source.
• C. 48 A multiplies 12 V by 4 Ω; the short-circuit current is found by dividing.