A voltage source connected in series with a resistor can be converted to a?

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Examoogle · Accepted Answer

Current source in parallel with a resistor

Explanation: A voltage source in series with a resistor can be transformed into an equivalent current source in parallel with the same resistor using Source Transformation. This technique maintains identical terminal characteristics for any load connected to the circuit.

Working Principle: The transformation is based on Ohm's Law where $I = \frac{V}{R}$. The voltage source $V$ in series with $R$ behaves exactly like a current source $I = \frac{V}{R}$ in parallel with the same resistor $R$. The polarity of the current source points toward the positive terminal of the original voltage source.

Key Formulas: $I = \frac{V}{R}$ — Current source value; $V = I 	imes R$ — Voltage source value

Key Points: Source transformation is valid only if the internal resistance remains the same in both configurations.; The arrow of the current source points in the direction of the voltage source's positive terminal.; This method simplifies nodal and mesh analysis by reducing the number of components.

Advantages: Simplifies complex circuit analysis; Allows conversion between Norton and Thevenin equivalents

Disadvantages: Does not apply to independent sources without internal resistance; Cannot be used if the internal resistance is zero (ideal voltage source)

Applications: Circuit simplification for Nodal Analysis; Circuit simplification for Mesh Analysis

Additional Info: This is known as the Source Transformation Theorem.. Option A is incorrect because current sources must be in parallel with internal resistance for equivalence.. Option C describes a configuration that does not maintain terminal equivalence.

Answer: B is correct — A voltage source in series with a resistor is equivalent to a current source of value $I = \frac{V}{R}$ in parallel with the same resistor $R$.

Exam Tip: When performing source transformation, always check if the internal resistance is in series with the voltage source or in parallel with the current source before starting your calculations.

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